Daily Papers

Offline multi-agent reinforcement learning is challenging due to the coupling effect of both distribution shift issue common in offline setting and the high dimension issue common in multi-agent setting, making the action out-of-distribution (OOD) and value overestimation phenomenon excessively severe. Tomitigate this problem, we propose a novel multi-agent offline RL algorithm, named CounterFactual Conservative Q-Learning (CFCQL) to conduct conservative value estimation. Rather than regarding all the agents as a high dimensional single one and directly applying single agent methods to it, CFCQL calculates conservative regularization for each agent separately in a counterfactual way and then linearly combines them to realize an overall conservative value estimation. We prove that it still enjoys the underestimation property and the performance guarantee as those single agent conservative methods do, but the induced regularization and safe policy improvement bound are independent of the agent number, which is therefore theoretically superior to the direct treatment referred to above, especially when the agent number is large. We further conduct experiments on four environments including both discrete and continuous action settings on both existing and our man-made datasets, demonstrating that CFCQL outperforms existing methods on most datasets and even with a remarkable margin on some of them.

As Reinforcement Learning (RL) agents are increasingly employed in diverse decision-making problems using reward preferences, it becomes important to ensure that policies learned by these frameworks in mapping observations to a probability distribution of the possible actions are explainable. However, there is little to no work in the systematic understanding of these complex policies in a contrastive manner, i.e., what minimal changes to the policy would improve/worsen its performance to a desired level. In this work, we present COUNTERPOL, the first framework to analyze RL policies using counterfactual explanations in the form of minimal changes to the policy that lead to the desired outcome. We do so by incorporating counterfactuals in supervised learning in RL with the target outcome regulated using desired return. We establish a theoretical connection between Counterpol and widely used trust region-based policy optimization methods in RL. Extensive empirical analysis shows the efficacy of COUNTERPOL in generating explanations for (un)learning skills while keeping close to the original policy. Our results on five different RL environments with diverse state and action spaces demonstrate the utility of counterfactual explanations, paving the way for new frontiers in designing and developing counterfactual policies.

Offline reinforcement learning faces a significant challenge of value over-estimation due to the distributional drift between the dataset and the current learned policy, leading to learning failure in practice. The common approach is to incorporate a penalty term to reward or value estimation in the Bellman iterations. Meanwhile, to avoid extrapolation on out-of-distribution (OOD) states and actions, existing methods focus on conservative Q-function estimation. In this paper, we propose Conservative State Value Estimation (CSVE), a new approach that learns conservative V-function via directly imposing penalty on OOD states. Compared to prior work, CSVE allows more effective in-data policy optimization with conservative value guarantees. Further, we apply CSVE and develop a practical actor-critic algorithm in which the critic does the conservative value estimation by additionally sampling and penalizing the states around the dataset, and the actor applies advantage weighted updates extended with state exploration to improve the policy. We evaluate in classic continual control tasks of D4RL, showing that our method performs better than the conservative Q-function learning methods and is strongly competitive among recent SOTA methods.

Offline reinforcement learning learns an effective policy on offline datasets without online interaction, and it attracts persistent research attention due to its potential of practical application. However, extrapolation error generated by distribution shift will still lead to the overestimation for those actions that transit to out-of-distribution(OOD) states, which degrades the reliability and robustness of the offline policy. In this paper, we propose Contextual Conservative Q-Learning(C-CQL) to learn a robustly reliable policy through the contextual information captured via an inverse dynamics model. With the supervision of the inverse dynamics model, it tends to learn a policy that generates stable transition at perturbed states, for the fact that pertuebed states are a common kind of OOD states. In this manner, we enable the learnt policy more likely to generate transition that destines to the empirical next state distributions of the offline dataset, i.e., robustly reliable transition. Besides, we theoretically reveal that C-CQL is the generalization of the Conservative Q-Learning(CQL) and aggressive State Deviation Correction(SDC). Finally, experimental results demonstrate the proposed C-CQL achieves the state-of-the-art performance in most environments of offline Mujoco suite and a noisy Mujoco setting.

A good model for action-effect prediction, named environment model, is important to achieve sample-efficient decision-making policy learning in many domains like robot control, recommender systems, and patients' treatment selection. We can take unlimited trials with such a model to identify the appropriate actions so that the costs of queries in the real world can be saved. It requires the model to handle unseen data correctly, also called counterfactual data. However, standard data fitting techniques do not automatically achieve such generalization ability and commonly result in unreliable models. In this work, we introduce counterfactual-query risk minimization (CQRM) in model learning for generalizing to a counterfactual dataset queried by a specific target policy. Since the target policies can be various and unknown in policy learning, we propose an adversarial CQRM objective in which the model learns on counterfactual data queried by adversarial policies, and finally derive a tractable solution GALILEO. We also discover that adversarial CQRM is closely related to the adversarial model learning, explaining the effectiveness of the latter. We apply GALILEO in synthetic tasks and a real-world application. The results show that GALILEO makes accurate predictions on counterfactual data and thus significantly improves policies in real-world testing.

Offline reinforcement learning (RL) provides a promising direction to exploit massive amount of offline data for complex decision-making tasks. Due to the distribution shift issue, current offline RL algorithms are generally designed to be conservative in value estimation and action selection. However, such conservatism can impair the robustness of learned policies when encountering observation deviation under realistic conditions, such as sensor errors and adversarial attacks. To trade off robustness and conservatism, we propose Robust Offline Reinforcement Learning (RORL) with a novel conservative smoothing technique. In RORL, we explicitly introduce regularization on the policy and the value function for states near the dataset, as well as additional conservative value estimation on these states. Theoretically, we show RORL enjoys a tighter suboptimality bound than recent theoretical results in linear MDPs. We demonstrate that RORL can achieve state-of-the-art performance on the general offline RL benchmark and is considerably robust to adversarial observation perturbations.

Zero-shot reinforcement learning (RL) promises to provide agents that can perform any task in an environment after an offline pre-training phase. Forward-backward (FB) representations represent remarkable progress towards this ideal, achieving 85% of the performance of task-specific agents in this setting. However, such performance is contingent on access to large and diverse datasets for pre-training, which cannot be expected for most real problems. Here, we explore how FB performance degrades when trained on small datasets that lack diversity, and mitigate it with conservatism, a well-established feature of performant offline RL algorithms. We evaluate our family of methods across various datasets, domains and tasks, reaching 150% of vanilla FB performance in aggregate. Somewhat surprisingly, conservative FB algorithms also outperform the task-specific baseline, despite lacking access to reward labels and being required to maintain policies for all tasks. Conservative FB algorithms perform no worse than FB on full datasets, and so present little downside over their predecessor. Our code is available open-source via https://enjeeneer.io/projects/conservative-world-models/.

Provably efficient Model-Based Reinforcement Learning (MBRL) based on optimism or posterior sampling (PSRL) is ensured to attain the global optimality asymptotically by introducing the complexity measure of the model. However, the complexity might grow exponentially for the simplest nonlinear models, where global convergence is impossible within finite iterations. When the model suffers a large generalization error, which is quantitatively measured by the model complexity, the uncertainty can be large. The sampled model that current policy is greedily optimized upon will thus be unsettled, resulting in aggressive policy updates and over-exploration. In this work, we propose Conservative Dual Policy Optimization (CDPO) that involves a Referential Update and a Conservative Update. The policy is first optimized under a reference model, which imitates the mechanism of PSRL while offering more stability. A conservative range of randomness is guaranteed by maximizing the expectation of model value. Without harmful sampling procedures, CDPO can still achieve the same regret as PSRL. More importantly, CDPO enjoys monotonic policy improvement and global optimality simultaneously. Empirical results also validate the exploration efficiency of CDPO.

Popular offline reinforcement learning (RL) methods rely on conservatism, either by penalizing out-of-dataset actions or by restricting rollout horizons. In this work, we question the universality of this principle and instead revisit a complementary one: a Bayesian perspective. Rather than enforcing conservatism, the Bayesian approach tackles epistemic uncertainty in offline data by modeling a posterior distribution over plausible world models and training a history-dependent agent to maximize expected rewards, enabling test-time generalization. We first illustrate, in a bandit setting, that Bayesianism excels on low-quality datasets where conservatism fails. We then scale this principle to realistic tasks and show that long-horizon planning is critical for reducing value overestimation once conservatism is removed. To make this feasible, we introduce key design choices for performing and learning from long-horizon rollouts while controlling compounding errors. These yield our algorithm, NEUBAY, grounded in the neutral Bayesian principle. On D4RL and NeoRL benchmarks, NEUBAY generally matches or surpasses leading conservative algorithms, achieving new state-of-the-art on 7 datasets. Notably, it succeeds with rollout horizons of several hundred steps, contrary to dominant practice. Finally, we characterize datasets by quality and coverage, showing when NEUBAY is preferable to conservative methods. Together, we argue NEUBAY lays the foundation for a new practical direction in offline and model-based RL.

When applying offline reinforcement learning (RL) in healthcare scenarios, the out-of-distribution (OOD) issues pose significant risks, as inappropriate generalization beyond clinical expertise can result in potentially harmful recommendations. While existing methods like conservative Q-learning (CQL) attempt to address the OOD issue, their effectiveness is limited by only constraining action selection by suppressing uncertain actions. This action-only regularization imitates clinician actions that prioritize short-term rewards, but it fails to regulate downstream state trajectories, thereby limiting the discovery of improved long-term treatment strategies. To safely improve policy beyond clinician recommendations while ensuring that state-action trajectories remain in-distribution, we propose Offline Guarded Safe Reinforcement Learning (OGSRL), a theoretically grounded model-based offline RL framework. OGSRL introduces a novel dual constraint mechanism for improving policy with reliability and safety. First, the OOD guardian is established to specify clinically validated regions for safe policy exploration. By constraining optimization within these regions, it enables the reliable exploration of treatment strategies that outperform clinician behavior by leveraging the full patient state history, without drifting into unsupported state-action trajectories. Second, we introduce a safety cost constraint that encodes medical knowledge about physiological safety boundaries, providing domain-specific safeguards even in areas where training data might contain potentially unsafe interventions. Notably, we provide theoretical guarantees on safety and near-optimality: policies that satisfy these constraints remain in safe and reliable regions and achieve performance close to the best possible policy supported by the data.

Off-policy multi-step reinforcement learning algorithms consist of conservative and non-conservative algorithms: the former actively cut traces, whereas the latter do not. Recently, Munos et al. (2016) proved the convergence of conservative algorithms to an optimal Q-function. In contrast, non-conservative algorithms are thought to be unsafe and have a limited or no theoretical guarantee. Nonetheless, recent studies have shown that non-conservative algorithms empirically outperform conservative ones. Motivated by the empirical results and the lack of theory, we carry out theoretical analyses of Peng's Q(λ), a representative example of non-conservative algorithms. We prove that it also converges to an optimal policy provided that the behavior policy slowly tracks a greedy policy in a way similar to conservative policy iteration. Such a result has been conjectured to be true but has not been proven. We also experiment with Peng's Q(λ) in complex continuous control tasks, confirming that Peng's Q(λ) often outperforms conservative algorithms despite its simplicity. These results indicate that Peng's Q(λ), which was thought to be unsafe, is a theoretically-sound and practically effective algorithm.

We improve the framework of open games with agency by showing how the players' counterfactual analysis giving rise to Nash equilibria can be described in the dynamics of the game itself (hence diegetically), getting rid of devices such as equilibrium predicates. This new approach overlaps almost completely with the way gradient-based learners are specified and trained. Indeed, we show feedback propagation in games can be seen as a form of backpropagation, with a crucial difference explaining the distinctive character of the phenomenology of non-cooperative games. We outline a functorial construction of arena of games, show players form a subsystem over it, and prove that their 'fixpoint behaviours' are Nash equilibria.

Imitation learning suffers from causal confusion. This phenomenon occurs when learned policies attend to features that do not causally influence the expert actions but are instead spuriously correlated. Causally confused agents produce low open-loop supervised loss but poor closed-loop performance upon deployment. We consider the problem of masking observed confounders in a disentangled representation of the observation space. Our novel masking algorithm leverages the usual ability to intervene in the initial system state, avoiding any requirement involving expert querying, expert reward functions, or causal graph specification. Under certain assumptions, we theoretically prove that this algorithm is conservative in the sense that it does not incorrectly mask observations that causally influence the expert; furthermore, intervening on the initial state serves to strictly reduce excess conservatism. The masking algorithm is applied to behavior cloning for two illustrative control systems: CartPole and Reacher.

Card games are widely used to study sequential decision-making under uncertainty, with real-world analogues in negotiation, finance, and cybersecurity. These games typically fall into three categories based on the flow of control: strictly sequential (players alternate single actions), deterministic response (some actions trigger a fixed outcome), and unbounded reciprocal response (alternating counterplays are permitted). A less-explored but strategically rich structure is the bounded one-sided response, where a player's action briefly transfers control to the opponent, who must satisfy a fixed condition through one or more moves before the turn resolves. We term games featuring this mechanism Bounded One-Sided Response Games (BORGs). We introduce a modified version of Monopoly Deal as a benchmark environment that isolates this dynamic, where a Rent action forces the opponent to choose payment assets. The gold-standard algorithm, Counterfactual Regret Minimization (CFR), converges on effective strategies without novel algorithmic extensions. A lightweight full-stack research platform unifies the environment, a parallelized CFR runtime, and a human-playable web interface. The trained CFR agent and source code are available at https://monopolydeal.ai.

Offline reinforcement learning (RL) holds promise as a means to learn high-reward policies from a static dataset, without the need for further environment interactions. However, a key challenge in offline RL lies in effectively stitching portions of suboptimal trajectories from the static dataset while avoiding extrapolation errors arising due to a lack of support in the dataset. Existing approaches use conservative methods that are tricky to tune and struggle with multi-modal data (as we show) or rely on noisy Monte Carlo return-to-go samples for reward conditioning. In this work, we propose a novel approach that leverages the expressiveness of latent diffusion to model in-support trajectory sequences as compressed latent skills. This facilitates learning a Q-function while avoiding extrapolation error via batch-constraining. The latent space is also expressive and gracefully copes with multi-modal data. We show that the learned temporally-abstract latent space encodes richer task-specific information for offline RL tasks as compared to raw state-actions. This improves credit assignment and facilitates faster reward propagation during Q-learning. Our method demonstrates state-of-the-art performance on the D4RL benchmarks, particularly excelling in long-horizon, sparse-reward tasks.

Counterfactual reasoning, a hallmark of intelligence, consists of three steps: inferring latent variables from observations (abduction), constructing alternatives (interventions), and predicting their outcomes (prediction). This skill is essential for advancing LLMs' causal understanding and expanding their applications in high-stakes domains such as scientific research. However, existing efforts in assessing LLM's counterfactual reasoning capabilities tend to skip the abduction step, effectively reducing to interventional reasoning and leading to overestimation of LLM performance. To address this, we introduce executable counterfactuals, a novel framework that operationalizes causal reasoning through code and math problems. Our framework explicitly requires all three steps of counterfactual reasoning and enables scalable synthetic data creation with varying difficulty, creating a frontier for evaluating and improving LLM's reasoning. Our results reveal substantial drop in accuracy (25-40%) from interventional to counterfactual reasoning for SOTA models like o4-mini and Claude-4-Sonnet. To address this gap, we construct a training set comprising counterfactual code problems having if-else condition and test on out-of-domain code structures (e.g. having while-loop); we also test whether a model trained on code would generalize to counterfactual math word problems. While supervised finetuning on stronger models' reasoning traces improves in-domain performance of Qwen models, it leads to a decrease in accuracy on OOD tasks such as counterfactual math problems. In contrast, reinforcement learning induces the core cognitive behaviors and generalizes to new domains, yielding gains over the base model on both code (improvement of 1.5x-2x) and math problems. Analysis of the reasoning traces reinforces these findings and highlights the promise of RL for improving LLMs' counterfactual reasoning.

Primal-dual safe RL methods commonly perform iterations between the primal update of the policy and the dual update of the Lagrange Multiplier. Such a training paradigm is highly susceptible to the error in cumulative cost estimation since this estimation serves as the key bond connecting the primal and dual update processes. We show that this problem causes significant underestimation of cost when using off-policy methods, leading to the failure to satisfy the safety constraint. To address this issue, we propose conservative policy optimization, which learns a policy in a constraint-satisfying area by considering the uncertainty in cost estimation. This improves constraint satisfaction but also potentially hinders reward maximization. We then introduce local policy convexification to help eliminate such suboptimality by gradually reducing the estimation uncertainty. We provide theoretical interpretations of the joint coupling effect of these two ingredients and further verify them by extensive experiments. Results on benchmark tasks show that our method not only achieves an asymptotic performance comparable to state-of-the-art on-policy methods while using much fewer samples, but also significantly reduces constraint violation during training. Our code is available at https://github.com/ZifanWu/CAL.

Reinforcement learning from human feedback (RLHF) is a standard approach for fine-tuning large language models to follow instructions. As part of this process, learned reward models are used to approximately model human preferences. However, as imperfect representations of the "true" reward, these learned reward models are susceptible to overoptimization. Gao et al. (2023) studied this phenomenon in a synthetic human feedback setup with a significantly larger "gold" reward model acting as the true reward (instead of humans) and showed that overoptimization remains a persistent problem regardless of the size of the proxy reward model and training data used. Using a similar setup, we conduct a systematic study to evaluate the efficacy of using ensemble-based conservative optimization objectives, specifically worst-case optimization (WCO) and uncertainty-weighted optimization (UWO), for mitigating reward model overoptimization when using two optimization methods: (a) best-of-n sampling (BoN) (b) proximal policy optimization (PPO). We additionally extend the setup of Gao et al. (2023) to include 25% label noise to better mirror real-world conditions. Both with and without label noise, we find that conservative optimization practically eliminates overoptimization and improves performance by up to 70% for BoN sampling. For PPO, ensemble-based conservative optimization always reduces overoptimization and outperforms single reward model optimization. Moreover, combining it with a small KL penalty successfully prevents overoptimization at no performance cost. Overall, our results demonstrate that ensemble-based conservative optimization can effectively counter overoptimization.

We provide an optimization-based framework to perform counterfactual analysis in a dynamic model with hidden states. Our framework is grounded in the ``abduction, action, and prediction'' approach to answer counterfactual queries and handles two key challenges where (1) the states are hidden and (2) the model is dynamic. Recognizing the lack of knowledge on the underlying causal mechanism and the possibility of infinitely many such mechanisms, we optimize over this space and compute upper and lower bounds on the counterfactual quantity of interest. Our work brings together ideas from causality, state-space models, simulation, and optimization, and we apply it on a breast cancer case study. To the best of our knowledge, we are the first to compute lower and upper bounds on a counterfactual query in a dynamic latent-state model.

Counterfactual explanations are attracting significant attention due to the flourishing applications of machine learning models in consequential domains. A counterfactual plan consists of multiple possibilities to modify a given instance so that the model's prediction will be altered. As the predictive model can be updated subject to the future arrival of new data, a counterfactual plan may become ineffective or infeasible with respect to the future values of the model parameters. In this work, we study the counterfactual plans under model uncertainty, in which the distribution of the model parameters is partially prescribed using only the first- and second-moment information. First, we propose an uncertainty quantification tool to compute the lower and upper bounds of the probability of validity for any given counterfactual plan. We then provide corrective methods to adjust the counterfactual plan to improve the validity measure. The numerical experiments validate our bounds and demonstrate that our correction increases the robustness of the counterfactual plans in different real-world datasets.

Offline reinforcement learning (RL) is a compelling framework for learning optimal policies from past experiences without additional interaction with the environment. Nevertheless, offline RL inevitably faces the problem of distributional shifts, where the states and actions encountered during policy execution may not be in the training dataset distribution. A common solution involves incorporating conservatism into the policy or the value function to safeguard against uncertainties and unknowns. In this work, we focus on achieving the same objectives of conservatism but from a different perspective. We propose COmpositional COnservatism with Anchor-seeking (COCOA) for offline RL, an approach that pursues conservatism in a compositional manner on top of the transductive reparameterization (Netanyahu et al., 2023), which decomposes the input variable (the state in our case) into an anchor and its difference from the original input. Our COCOA seeks both in-distribution anchors and differences by utilizing the learned reverse dynamics model, encouraging conservatism in the compositional input space for the policy or value function. Such compositional conservatism is independent of and agnostic to the prevalent behavioral conservatism in offline RL. We apply COCOA to four state-of-the-art offline RL algorithms and evaluate them on the D4RL benchmark, where COCOA generally improves the performance of each algorithm. The code is available at https://github.com/runamu/compositional-conservatism.

Offline reinforcement learning (RL) offers a promising direction for learning policies from pre-collected datasets without requiring further interactions with the environment. However, existing methods struggle to handle out-of-distribution (OOD) extrapolation errors, especially in sparse reward or scarce data settings. In this paper, we propose a novel training algorithm called Conservative Density Estimation (CDE), which addresses this challenge by explicitly imposing constraints on the state-action occupancy stationary distribution. CDE overcomes the limitations of existing approaches, such as the stationary distribution correction method, by addressing the support mismatch issue in marginal importance sampling. Our method achieves state-of-the-art performance on the D4RL benchmark. Notably, CDE consistently outperforms baselines in challenging tasks with sparse rewards or insufficient data, demonstrating the advantages of our approach in addressing the extrapolation error problem in offline RL.

Recent advances in large language models (LLMs) have demonstrated significant progress in performing complex tasks. While Reinforcement Learning from Human Feedback (RLHF) has been effective in aligning LLMs with human preferences, it is susceptible to spurious correlations in reward modeling. Consequently, it often introduces biases-such as length bias, sycophancy, conceptual bias, and discrimination that hinder the model's ability to capture true causal relationships. To address this, we propose a novel causal reward modeling approach that integrates causal inference to mitigate these spurious correlations. Our method enforces counterfactual invariance, ensuring reward predictions remain consistent when irrelevant variables are altered. Through experiments on both synthetic and real-world datasets, we show that our approach mitigates various types of spurious correlations effectively, resulting in more reliable and fair alignment of LLMs with human preferences. As a drop-in enhancement to the existing RLHF workflow, our causal reward modeling provides a practical way to improve the trustworthiness and fairness of LLM finetuning.

Much of the advancement of Multi-Agent Reinforcement Learning (MARL) in imperfect-information games has historically depended on manual iterative refinement of baselines. While foundational families like Counterfactual Regret Minimization (CFR) and Policy Space Response Oracles (PSRO) rest on solid theoretical ground, the design of their most effective variants often relies on human intuition to navigate a vast algorithmic design space. In this work, we propose the use of AlphaEvolve, an evolutionary coding agent powered by large language models, to automatically discover new multiagent learning algorithms. We demonstrate the generality of this framework by evolving novel variants for two distinct paradigms of game-theoretic learning. First, in the domain of iterative regret minimization, we evolve the logic governing regret accumulation and policy derivation, discovering a new algorithm, Volatility-Adaptive Discounted (VAD-)CFR. VAD-CFR employs novel, non-intuitive mechanisms-including volatility-sensitive discounting, consistency-enforced optimism, and a hard warm-start policy accumulation schedule-to outperform state-of-the-art baselines like Discounted Predictive CFR+. Second, in the regime of population based training algorithms, we evolve training-time and evaluation-time meta strategy solvers for PSRO, discovering a new variant, Smoothed Hybrid Optimistic Regret (SHOR-)PSRO. SHOR-PSRO introduces a hybrid meta-solver that linearly blends Optimistic Regret Matching with a smoothed, temperature-controlled distribution over best pure strategies. By dynamically annealing this blending factor and diversity bonuses during training, the algorithm automates the transition from population diversity to rigorous equilibrium finding, yielding superior empirical convergence compared to standard static meta-solvers.

In this work, we study the simple yet universally applicable case of reward shaping in value-based Deep Reinforcement Learning (DRL). We show that reward shifting in the form of the linear transformation is equivalent to changing the initialization of the Q-function in function approximation. Based on such an equivalence, we bring the key insight that a positive reward shifting leads to conservative exploitation, while a negative reward shifting leads to curiosity-driven exploration. Accordingly, conservative exploitation improves offline RL value estimation, and optimistic value estimation improves exploration for online RL. We validate our insight on a range of RL tasks and show its improvement over baselines: (1) In offline RL, the conservative exploitation leads to improved performance based on off-the-shelf algorithms; (2) In online continuous control, multiple value functions with different shifting constants can be used to tackle the exploration-exploitation dilemma for better sample efficiency; (3) In discrete control tasks, a negative reward shifting yields an improvement over the curiosity-based exploration method.

This paper investigates conservative exploration in reinforcement learning where the performance of the learning agent is guaranteed to be above a certain threshold throughout the learning process. It focuses on the tabular episodic Markov Decision Process (MDP) setting that has finite states and actions. With the knowledge of an existing safe baseline policy, an algorithm termed as StepMix is proposed to balance the exploitation and exploration while ensuring that the conservative constraint is never violated in each episode with high probability. StepMix features a unique design of a mixture policy that adaptively and smoothly interpolates between the baseline policy and the optimistic policy. Theoretical analysis shows that StepMix achieves near-optimal regret order as in the constraint-free setting, indicating that obeying the stringent episode-wise conservative constraint does not compromise the learning performance. Besides, a randomization-based EpsMix algorithm is also proposed and shown to achieve the same performance as StepMix. The algorithm design and theoretical analysis are further extended to the setting where the baseline policy is not given a priori but must be learned from an offline dataset, and it is proved that similar conservative guarantee and regret can be achieved if the offline dataset is sufficiently large. Experiment results corroborate the theoretical analysis and demonstrate the effectiveness of the proposed conservative exploration strategies.

In Causal Bayesian Optimization (CBO), an agent intervenes on an unknown structural causal model to maximize a downstream reward variable. In this paper, we consider the generalization where other agents or external events also intervene on the system, which is key for enabling adaptiveness to non-stationarities such as weather changes, market forces, or adversaries. We formalize this generalization of CBO as Adversarial Causal Bayesian Optimization (ACBO) and introduce the first algorithm for ACBO with bounded regret: Causal Bayesian Optimization with Multiplicative Weights (CBO-MW). Our approach combines a classical online learning strategy with causal modeling of the rewards. To achieve this, it computes optimistic counterfactual reward estimates by propagating uncertainty through the causal graph. We derive regret bounds for CBO-MW that naturally depend on graph-related quantities. We further propose a scalable implementation for the case of combinatorial interventions and submodular rewards. Empirically, CBO-MW outperforms non-causal and non-adversarial Bayesian optimization methods on synthetic environments and environments based on real-word data. Our experiments include a realistic demonstration of how CBO-MW can be used to learn users' demand patterns in a shared mobility system and reposition vehicles in strategic areas.

A key challenge in the field of reinforcement learning is to develop agents that behave cautiously in novel situations. It is generally impossible to anticipate all situations that an autonomous system may face or what behavior would best avoid bad outcomes. An agent that can learn to be cautious would overcome this challenge by discovering for itself when and how to behave cautiously. In contrast, current approaches typically embed task-specific safety information or explicit cautious behaviors into the system, which is error-prone and imposes extra burdens on practitioners. In this paper, we present both a sequence of tasks where cautious behavior becomes increasingly non-obvious, as well as an algorithm to demonstrate that it is possible for a system to learn to be cautious. The essential features of our algorithm are that it characterizes reward function uncertainty without task-specific safety information and uses this uncertainty to construct a robust policy. Specifically, we construct robust policies with a k-of-N counterfactual regret minimization (CFR) subroutine given learned reward function uncertainty represented by a neural network ensemble. These policies exhibit caution in each of our tasks without any task-specific safety tuning. Our code is available at https://github.com/montaserFath/Learning-to-be-Cautious

Answering counterfactual queries has many important applications such as knowledge discovery and explainability, but is challenging when causal variables are unobserved and we only see a projection onto an observation space, for instance, image pixels. One approach is to recover the latent Structural Causal Model (SCM), but this typically needs unrealistic assumptions, such as linearity of the causal mechanisms. Another approach is to use na\"ive ML approximations, such as generative models, to generate counterfactual samples; however, these lack guarantees of accuracy. In this work, we strive to strike a balance between practicality and theoretical guarantees by focusing on a specific type of causal query called domain counterfactuals, which hypothesizes what a sample would have looked like if it had been generated in a different domain (or environment). Concretely, by only assuming invertibility, sparse domain interventions and access to observational data from different domains, we aim to improve domain counterfactual estimation both theoretically and practically with less restrictive assumptions. We define domain counterfactually equivalent models and prove necessary and sufficient properties for equivalent models that provide a tight characterization of the domain counterfactual equivalence classes. Building upon this result, we prove that every equivalence class contains a model where all intervened variables are at the end when topologically sorted by the causal DAG. This surprising result suggests that a model design that only allows intervention in the last k latent variables may improve model estimation for counterfactuals. We then test this model design on extensive simulated and image-based experiments which show the sparse canonical model indeed improves counterfactual estimation over baseline non-sparse models.

There is an emerging interest in generating robust counterfactual explanations that would remain valid if the model is updated or changed even slightly. Towards finding robust counterfactuals, existing literature often assumes that the original model m and the new model M are bounded in the parameter space, i.e., |Params(M){-}Params(m)|{<}Delta. However, models can often change significantly in the parameter space with little to no change in their predictions or accuracy on the given dataset. In this work, we introduce a mathematical abstraction termed naturally-occurring model change, which allows for arbitrary changes in the parameter space such that the change in predictions on points that lie on the data manifold is limited. Next, we propose a measure -- that we call Stability -- to quantify the robustness of counterfactuals to potential model changes for differentiable models, e.g., neural networks. Our main contribution is to show that counterfactuals with sufficiently high value of Stability as defined by our measure will remain valid after potential ``naturally-occurring'' model changes with high probability (leveraging concentration bounds for Lipschitz function of independent Gaussians). Since our quantification depends on the local Lipschitz constant around a data point which is not always available, we also examine practical relaxations of our proposed measure and demonstrate experimentally how they can be incorporated to find robust counterfactuals for neural networks that are close, realistic, and remain valid after potential model changes.

Users of music streaming, video streaming, news recommendation, and e-commerce services often engage with content in a sequential manner. Providing and evaluating good sequences of recommendations is therefore a central problem for these services. Prior reweighting-based counterfactual evaluation methods either suffer from high variance or make strong independence assumptions about rewards. We propose a new counterfactual estimator that allows for sequential interactions in the rewards with lower variance in an asymptotically unbiased manner. Our method uses graphical assumptions about the causal relationships of the slate to reweight the rewards in the logging policy in a way that approximates the expected sum of rewards under the target policy. Extensive experiments in simulation and on a live recommender system show that our approach outperforms existing methods in terms of bias and data efficiency for the sequential track recommendations problem.

The offline reinforcement learning (RL) paradigm provides a general recipe to convert static behavior datasets into policies that can perform better than the policy that collected the data. While policy constraints, conservatism, and other methods for mitigating distributional shifts have made offline reinforcement learning more effective, the continuous action setting often necessitates various approximations for applying these techniques. Many of these challenges are greatly alleviated in discrete action settings, where offline RL constraints and regularizers can often be computed more precisely or even exactly. In this paper, we propose an adaptive scheme for action quantization. We use a VQ-VAE to learn state-conditioned action quantization, avoiding the exponential blowup that comes with na\"ive discretization of the action space. We show that several state-of-the-art offline RL methods such as IQL, CQL, and BRAC improve in performance on benchmarks when combined with our proposed discretization scheme. We further validate our approach on a set of challenging long-horizon complex robotic manipulation tasks in the Robomimic environment, where our discretized offline RL algorithms are able to improve upon their continuous counterparts by 2-3x. Our project page is at https://saqrl.github.io/

Linear temporal logic (LTL) offers a simplified way of specifying tasks for policy optimization that may otherwise be difficult to describe with scalar reward functions. However, the standard RL framework can be too myopic to find maximally LTL satisfying policies. This paper makes two contributions. First, we develop a new value-function based proxy, using a technique we call eventual discounting, under which one can find policies that satisfy the LTL specification with highest achievable probability. Second, we develop a new experience replay method for generating off-policy data from on-policy rollouts via counterfactual reasoning on different ways of satisfying the LTL specification. Our experiments, conducted in both discrete and continuous state-action spaces, confirm the effectiveness of our counterfactual experience replay approach.

Offline reinforcement learning (RL) is a challenging setting where existing off-policy actor-critic methods perform poorly due to the overestimation of out-of-distribution state-action pairs. Thus, various additional augmentations are proposed to keep the learned policy close to the offline dataset (or the behavior policy). In this work, starting from the analysis of offline monotonic policy improvement, we get a surprising finding that some online on-policy algorithms are naturally able to solve offline RL. Specifically, the inherent conservatism of these on-policy algorithms is exactly what the offline RL method needs to overcome the overestimation. Based on this, we propose Behavior Proximal Policy Optimization (BPPO), which solves offline RL without any extra constraint or regularization introduced compared to PPO. Extensive experiments on the D4RL benchmark indicate this extremely succinct method outperforms state-of-the-art offline RL algorithms. Our implementation is available at https://github.com/Dragon-Zhuang/BPPO.

Counterfactual Risk Minimization (CRM) is a framework for dealing with the logged bandit feedback problem, where the goal is to improve a logging policy using offline data. In this paper, we explore the case where it is possible to deploy learned policies multiple times and acquire new data. We extend the CRM principle and its theory to this scenario, which we call "Sequential Counterfactual Risk Minimization (SCRM)." We introduce a novel counterfactual estimator and identify conditions that can improve the performance of CRM in terms of excess risk and regret rates, by using an analysis similar to restart strategies in accelerated optimization methods. We also provide an empirical evaluation of our method in both discrete and continuous action settings, and demonstrate the benefits of multiple deployments of CRM.

We introduce Iterated Bellman Calibration, a simple, model-agnostic, post-hoc procedure for calibrating off-policy value predictions in infinite-horizon Markov decision processes. Bellman calibration requires that states with similar predicted long-term returns exhibit one-step returns consistent with the Bellman equation under the target policy. We adapt classical histogram and isotonic calibration to the dynamic, counterfactual setting by repeatedly regressing fitted Bellman targets onto a model's predictions, using a doubly robust pseudo-outcome to handle off-policy data. This yields a one-dimensional fitted value iteration scheme that can be applied to any value estimator. Our analysis provides finite-sample guarantees for both calibration and prediction under weak assumptions, and critically, without requiring Bellman completeness or realizability.

A prominent challenge of offline reinforcement learning (RL) is the issue of hidden confounding: unobserved variables may influence both the actions taken by the agent and the observed outcomes. Hidden confounding can compromise the validity of any causal conclusion drawn from data and presents a major obstacle to effective offline RL. In the present paper, we tackle the problem of hidden confounding in the nonidentifiable setting. We propose a definition of uncertainty due to hidden confounding bias, termed delphic uncertainty, which uses variation over world models compatible with the observations, and differentiate it from the well-known epistemic and aleatoric uncertainties. We derive a practical method for estimating the three types of uncertainties, and construct a pessimistic offline RL algorithm to account for them. Our method does not assume identifiability of the unobserved confounders, and attempts to reduce the amount of confounding bias. We demonstrate through extensive experiments and ablations the efficacy of our approach on a sepsis management benchmark, as well as on electronic health records. Our results suggest that nonidentifiable hidden confounding bias can be mitigated to improve offline RL solutions in practice.

Distribution shift is a major obstacle in offline reinforcement learning, which necessitates minimizing the discrepancy between the learned policy and the behavior policy to avoid overestimating rare or unseen actions. Previous conservative offline RL algorithms struggle to generalize to unseen actions, despite their success in learning good in-distribution policy. In contrast, we propose to use the gradient fields of the dataset density generated from a pre-trained offline RL algorithm to adjust the original actions. We decouple the conservatism constraints from the policy, thus can benefit wide offline RL algorithms. As a consequence, we propose the Conservative Denoising Score-based Algorithm (CDSA) which utilizes the denoising score-based model to model the gradient of the dataset density, rather than the dataset density itself, and facilitates a more accurate and efficient method to adjust the action generated by the pre-trained policy in a deterministic and continuous MDP environment. In experiments, we show that our approach significantly improves the performance of baseline algorithms in D4RL datasets, and demonstrate the generalizability and plug-and-play capability of our model across different pre-trained offline RL policy in different tasks. We also validate that the agent exhibits greater risk aversion after employing our method while showcasing its ability to generalize effectively across diverse tasks.

Offline reinforcement learning (RL) has progressed with return-conditioned supervised learning (RCSL), but its lack of stitching ability remains a limitation. We introduce Q-Aided Conditional Supervised Learning (QCS), which effectively combines the stability of RCSL with the stitching capability of Q-functions. By analyzing Q-function over-generalization, which impairs stable stitching, QCS adaptively integrates Q-aid into RCSL's loss function based on trajectory return. Empirical results show that QCS significantly outperforms RCSL and value-based methods, consistently achieving or exceeding the maximum trajectory returns across diverse offline RL benchmarks.

Counterfactual explanations is one of the post-hoc methods used to provide explainability to machine learning models that have been attracting attention in recent years. Most examples in the literature, address the problem of generating post-hoc explanations for black-box machine learning models after the rejection of a loan application. In contrast, in this work, we investigate mathematical programming formulations for scorecard models, a type of interpretable model predominant within the banking industry for lending. The proposed mixed-integer programming formulations combine objective functions to ensure close, realistic and sparse counterfactuals using multi-objective optimization techniques for a binary, probability or continuous outcome. Moreover, we extend these formulations to generate multiple optimal counterfactuals simultaneously while guaranteeing diversity. Experiments on two real-world datasets confirm that the presented approach can generate optimal diverse counterfactuals addressing desired properties with assumable CPU times for practice use.

Reinforcement Learning from Human Feedback (RLHF) has proven effective in aligning large language models with human intentions, yet it often relies on complex methodologies like Proximal Policy Optimization (PPO) that require extensive hyper-parameter tuning and present challenges in sample efficiency and stability. In this paper, we introduce Inverse-Q*, an innovative framework that transcends traditional RL methods by optimizing token-level reinforcement learning without the need for additional reward or value models. Inverse-Q* leverages direct preference optimization techniques but extends them by estimating the conditionally optimal policy directly from the model's responses, facilitating more granular and flexible policy shaping. Our approach reduces reliance on human annotation and external supervision, making it especially suitable for low-resource settings. We present extensive experimental results demonstrating that Inverse-Q* not only matches but potentially exceeds the effectiveness of PPO in terms of convergence speed and the alignment of model responses with human preferences. Our findings suggest that Inverse-Q* offers a practical and robust alternative to conventional RLHF approaches, paving the way for more efficient and adaptable model training approaches.

Reinforcement learning (RL) post-training is crucial for LLM alignment and reasoning, but existing policy-based methods, such as PPO and DPO, can fall short of fixing shortcuts inherited from pre-training. In this work, we introduce Qsharp, a value-based algorithm for KL-regularized RL that guides the reference policy using the optimal regularized Q function. We propose to learn the optimal Q function using distributional RL on an aggregated online dataset. Unlike prior value-based baselines that guide the model using unregularized Q-values, our method is theoretically principled and provably learns the optimal policy for the KL-regularized RL problem. Empirically, Qsharp outperforms prior baselines in math reasoning benchmarks while maintaining a smaller KL divergence to the reference policy. Theoretically, we establish a reduction from KL-regularized RL to no-regret online learning, providing the first bounds for deterministic MDPs under only realizability. Thanks to distributional RL, our bounds are also variance-dependent and converge faster when the reference policy has small variance. In sum, our results highlight Qsharp as an effective approach for post-training LLMs, offering both improved performance and theoretical guarantees. The code can be found at https://github.com/jinpz/q_sharp.

Q-learning played a foundational role in the field reinforcement learning (RL). However, TD algorithms with off-policy data, such as Q-learning, or nonlinear function approximation like deep neural networks require several additional tricks to stabilise training, primarily a large replay buffer and target networks. Unfortunately, the delayed updating of frozen network parameters in the target network harms the sample efficiency and, similarly, the large replay buffer introduces memory and implementation overheads. In this paper, we investigate whether it is possible to accelerate and simplify off-policy TD training while maintaining its stability. Our key theoretical result demonstrates for the first time that regularisation techniques such as LayerNorm can yield provably convergent TD algorithms without the need for a target network or replay buffer, even with off-policy data. Empirically, we find that online, parallelised sampling enabled by vectorised environments stabilises training without the need for a large replay buffer. Motivated by these findings, we propose PQN, our simplified deep online Q-Learning algorithm. Surprisingly, this simple algorithm is competitive with more complex methods like: Rainbow in Atari, PPO-RNN in Craftax, QMix in Smax, and can be up to 50x faster than traditional DQN without sacrificing sample efficiency. In an era where PPO has become the go-to RL algorithm, PQN reestablishes off-policy Q-learning as a viable alternative.

Improving the performance of pre-trained policies through online reinforcement learning (RL) is a critical yet challenging topic. Existing online RL fine-tuning methods require continued training with offline pretrained Q-functions for stability and performance. However, these offline pretrained Q-functions commonly underestimate state-action pairs beyond the offline dataset due to the conservatism in most offline RL methods, which hinders further exploration when transitioning from the offline to the online setting. Additionally, this requirement limits their applicability in scenarios where only pre-trained policies are available but pre-trained Q-functions are absent, such as in imitation learning (IL) pre-training. To address these challenges, we propose a method for efficient online RL fine-tuning using solely the offline pre-trained policy, eliminating reliance on pre-trained Q-functions. We introduce PORL (Policy-Only Reinforcement Learning Fine-Tuning), which rapidly initializes the Q-function from scratch during the online phase to avoid detrimental pessimism. Our method not only achieves competitive performance with advanced offline-to-online RL algorithms and online RL approaches that leverage data or policies prior, but also pioneers a new path for directly fine-tuning behavior cloning (BC) policies.

Counterfactual reasoning is widely recognized as one of the most challenging and intricate aspects of causality in artificial intelligence. In this paper, we evaluate the performance of large language models (LLMs) in counterfactual reasoning. In contrast to previous studies that primarily focus on commonsense causal reasoning, where LLMs often rely on prior knowledge for inference, we specifically assess their ability to perform counterfactual inference using a set of formal rules. To support this evaluation, we introduce a new benchmark dataset, CounterBench, comprising 1K counterfactual reasoning questions. The dataset is designed with varying levels of difficulty, diverse causal graph structures, distinct types of counterfactual questions, and multiple nonsensical name variants. Our experiments demonstrate that counterfactual reasoning poses a significant challenge for LLMs, with most models performing at levels comparable to random guessing. To enhance LLM's counterfactual reasoning ability, we propose a novel reasoning paradigm, CoIn, which guides LLMs through iterative reasoning and backtracking to systematically explore counterfactual solutions. Experimental results show that our method significantly improves LLM performance on counterfactual reasoning tasks and consistently enhances performance across different LLMs.Our dataset is available at https://huggingface.co/datasets/CounterBench/CounterBench.

Off-policy dynamic programming (DP) techniques such as Q-learning have proven to be important in sequential decision-making problems. In the presence of function approximation, however, these techniques often diverge due to the absence of Bellman completeness in the function classes considered, a crucial condition for the success of DP-based methods. In this paper, we show how off-policy learning techniques based on return-conditioned supervised learning (RCSL) are able to circumvent these challenges of Bellman completeness, converging under significantly more relaxed assumptions inherited from supervised learning. We prove there exists a natural environment in which if one uses two-layer multilayer perceptron as the function approximator, the layer width needs to grow linearly with the state space size to satisfy Bellman completeness while a constant layer width is enough for RCSL. These findings take a step towards explaining the superior empirical performance of RCSL methods compared to DP-based methods in environments with near-optimal datasets. Furthermore, in order to learn from sub-optimal datasets, we propose a simple framework called MBRCSL, granting RCSL methods the ability of dynamic programming to stitch together segments from distinct trajectories. MBRCSL leverages learned dynamics models and forward sampling to accomplish trajectory stitching while avoiding the need for Bellman completeness that plagues all dynamic programming algorithms. We propose both theoretical analysis and experimental evaluation to back these claims, outperforming state-of-the-art model-free and model-based offline RL algorithms across several simulated robotics problems.

Reinforcement learning from Human Feedback (RLHF) learns from preference signals, while standard Reinforcement Learning (RL) directly learns from reward signals. Preferences arguably contain less information than rewards, which makes preference-based RL seemingly more difficult. This paper theoretically proves that, for a wide range of preference models, we can solve preference-based RL directly using existing algorithms and techniques for reward-based RL, with small or no extra costs. Specifically, (1) for preferences that are drawn from reward-based probabilistic models, we reduce the problem to robust reward-based RL that can tolerate small errors in rewards; (2) for general arbitrary preferences where the objective is to find the von Neumann winner, we reduce the problem to multiagent reward-based RL which finds Nash equilibria for factored Markov games under a restricted set of policies. The latter case can be further reduce to adversarial MDP when preferences only depend on the final state. We instantiate all reward-based RL subroutines by concrete provable algorithms, and apply our theory to a large class of models including tabular MDPs and MDPs with generic function approximation. We further provide guarantees when K-wise comparisons are available.

Given a set of trajectories demonstrating the execution of a task safely in a constrained MDP with observable rewards but with unknown constraints and non-observable costs, we aim to find a policy that maximizes the likelihood of demonstrated trajectories trading the balance between being conservative and increasing significantly the likelihood of high-rewarding trajectories but with potentially unsafe steps. Having these objectives, we aim towards learning a policy that maximizes the probability of the most promising trajectories with respect to the demonstrations. In so doing, we formulate the ``promise" of individual state-action pairs in terms of Q values, which depend on task-specific rewards as well as on the assessment of states' safety, mixing expectations in terms of rewards and safety. This entails a safe Q-learning perspective of the inverse learning problem under constraints: The devised Safe Q Inverse Constrained Reinforcement Learning (SafeQIL) algorithm is compared to state-of-the art inverse constraint reinforcement learning algorithms to a set of challenging benchmark tasks, showing its merits.

Can classical game-theoretic frameworks be extended to capture the bounded rationality and causal reasoning of AI agents? We investigate this question by extending Causal Normal Form Games (CNFGs) to sequential settings, introducing Sequential Causal Multi-Agent Systems (S-CMAS) that incorporate Pearl's Causal Hierarchy across leader-follower interactions. While theoretically elegant -- we prove PSPACE-completeness, develop equilibrium refinements, and establish connections to signaling theory -- our comprehensive empirical investigation reveals a critical limitation: S-CNE provides zero welfare improvement over classical Stackelberg equilibrium across all tested scenarios. Through 50+ Monte Carlo simulations and hand-crafted synthetic examples, we demonstrate that backward induction with rational best-response eliminates any strategic advantage from causal layer distinctions. We construct a theoretical example illustrating conditions where benefits could emerge (ε-rational satisficing followers), though implementation confirms that even relaxed rationality assumptions prove insufficient when good instincts align with optimal play. This negative result provides valuable insight: classical game-theoretic extensions grounded in rational choice are fundamentally incompatible with causal reasoning advantages, motivating new theoretical frameworks beyond standard Nash equilibrium for agentic AI.

Recent improvements in conditional generative modeling have made it possible to generate high-quality images from language descriptions alone. We investigate whether these methods can directly address the problem of sequential decision-making. We view decision-making not through the lens of reinforcement learning (RL), but rather through conditional generative modeling. To our surprise, we find that our formulation leads to policies that can outperform existing offline RL approaches across standard benchmarks. By modeling a policy as a return-conditional diffusion model, we illustrate how we may circumvent the need for dynamic programming and subsequently eliminate many of the complexities that come with traditional offline RL. We further demonstrate the advantages of modeling policies as conditional diffusion models by considering two other conditioning variables: constraints and skills. Conditioning on a single constraint or skill during training leads to behaviors at test-time that can satisfy several constraints together or demonstrate a composition of skills. Our results illustrate that conditional generative modeling is a powerful tool for decision-making.

In many real-world multi-agent cooperative tasks, due to high cost and risk, agents cannot continuously interact with the environment and collect experiences during learning, but have to learn from offline datasets. However, the transition dynamics in the dataset of each agent can be much different from the ones induced by the learned policies of other agents in execution, creating large errors in value estimates. Consequently, agents learn uncoordinated low-performing policies. In this paper, we propose a framework for offline decentralized multi-agent reinforcement learning, which exploits value deviation and transition normalization to deliberately modify the transition probabilities. Value deviation optimistically increases the transition probabilities of high-value next states, and transition normalization normalizes the transition probabilities of next states. They together enable agents to learn high-performing and coordinated policies. Theoretically, we prove the convergence of Q-learning under the altered non-stationary transition dynamics. Empirically, we show that the framework can be easily built on many existing offline reinforcement learning algorithms and achieve substantial improvement in a variety of multi-agent tasks.

Two main challenges in Reinforcement Learning (RL) are designing appropriate reward functions and ensuring the safety of the learned policy. To address these challenges, we present a theoretical framework for Inverse Reinforcement Learning (IRL) in constrained Markov decision processes. From a convex-analytic perspective, we extend prior results on reward identifiability and generalizability to both the constrained setting and a more general class of regularizations. In particular, we show that identifiability up to potential shaping (Cao et al., 2021) is a consequence of entropy regularization and may generally no longer hold for other regularizations or in the presence of safety constraints. We also show that to ensure generalizability to new transition laws and constraints, the true reward must be identified up to a constant. Additionally, we derive a finite sample guarantee for the suboptimality of the learned rewards, and validate our results in a gridworld environment.

Designing control policies whose performance level is guaranteed to remain above a given threshold in a span of environments is a critical feature for the adoption of reinforcement learning (RL) in real-world applications. The search for such robust policies is a notoriously difficult problem, related to the so-called dynamic model of transition function uncertainty, where the environment dynamics are allowed to change at each time step. But in practical cases, one is rather interested in robustness to a span of static transition models throughout interaction episodes. The static model is known to be harder to solve than the dynamic one, and seminal algorithms, such as robust value iteration, as well as most recent works on deep robust RL, build upon the dynamic model. In this work, we propose to revisit the static model. We suggest an analysis of why solving the static model under some mild hypotheses is a reasonable endeavor, based on an equivalence with the dynamic model, and formalize the general intuition that robust MDPs can be solved by tackling a series of static problems. We introduce a generic meta-algorithm called IWOCS, which incrementally identifies worst-case transition models so as to guide the search for a robust policy. Discussion on IWOCS sheds light on new ways to decouple policy optimization and adversarial transition functions and opens new perspectives for analysis. We derive a deep RL version of IWOCS and demonstrate it is competitive with state-of-the-art algorithms on classical benchmarks.

Many policy optimization approaches in reinforcement learning incorporate a Kullback-Leilbler (KL) divergence to the previous policy, to prevent the policy from changing too quickly. This idea was initially proposed in a seminal paper on Conservative Policy Iteration, with approximations given by algorithms like TRPO and Munchausen Value Iteration (MVI). We continue this line of work by investigating a generalized KL divergence -- called the Tsallis KL divergence -- which use the q-logarithm in the definition. The approach is a strict generalization, as q = 1 corresponds to the standard KL divergence; q > 1 provides a range of new options. We characterize the types of policies learned under the Tsallis KL, and motivate when q >1 could be beneficial. To obtain a practical algorithm that incorporates Tsallis KL regularization, we extend MVI, which is one of the simplest approaches to incorporate KL regularization. We show that this generalized MVI(q) obtains significant improvements over the standard MVI(q = 1) across 35 Atari games.

Reinforcement learning (RL) for continuous control often requires large amounts of online interaction data. Value-based RL methods can mitigate this burden by offering relatively high sample efficiency. Some studies further enhance sample efficiency by incorporating offline demonstration data to "kick-start" training, achieving promising results in continuous control. However, they typically compute the Q-function independently for each action dimension, neglecting interdependencies and making it harder to identify optimal actions when learning from suboptimal data, such as non-expert demonstration and online-collected data during the training process. To address these issues, we propose Auto-Regressive Soft Q-learning (ARSQ), a value-based RL algorithm that models Q-values in a coarse-to-fine, auto-regressive manner. First, ARSQ decomposes the continuous action space into discrete spaces in a coarse-to-fine hierarchy, enhancing sample efficiency for fine-grained continuous control tasks. Next, it auto-regressively predicts dimensional action advantages within each decision step, enabling more effective decision-making in continuous control tasks. We evaluate ARSQ on two continuous control benchmarks, RLBench and D4RL, integrating demonstration data into online training. On D4RL, which includes non-expert demonstrations, ARSQ achieves an average 1.62times performance improvement over SOTA value-based baseline. On RLBench, which incorporates expert demonstrations, ARSQ surpasses various baselines, demonstrating its effectiveness in learning from suboptimal online-collected data. Project page is at https://sites.google.com/view/ar-soft-q

Explainability methods for NLP systems encounter a version of the fundamental problem of causal inference: for a given ground-truth input text, we never truly observe the counterfactual texts necessary for isolating the causal effects of model representations on outputs. In response, many explainability methods make no use of counterfactual texts, assuming they will be unavailable. In this paper, we show that robust causal explainability methods can be created using approximate counterfactuals, which can be written by humans to approximate a specific counterfactual or simply sampled using metadata-guided heuristics. The core of our proposal is the Causal Proxy Model (CPM). A CPM explains a black-box model N because it is trained to have the same actual input/output behavior as N while creating neural representations that can be intervened upon to simulate the counterfactual input/output behavior of N. Furthermore, we show that the best CPM for N performs comparably to N in making factual predictions, which means that the CPM can simply replace N, leading to more explainable deployed models. Our code is available at https://github.com/frankaging/Causal-Proxy-Model.

In value-based reinforcement learning methods such as deep Q-learning, function approximation errors are known to lead to overestimated value estimates and suboptimal policies. We show that this problem persists in an actor-critic setting and propose novel mechanisms to minimize its effects on both the actor and the critic. Our algorithm builds on Double Q-learning, by taking the minimum value between a pair of critics to limit overestimation. We draw the connection between target networks and overestimation bias, and suggest delaying policy updates to reduce per-update error and further improve performance. We evaluate our method on the suite of OpenAI gym tasks, outperforming the state of the art in every environment tested.

We consider offline reinforcement learning (RL) methods in possibly nonstationary environments. Many existing RL algorithms in the literature rely on the stationarity assumption that requires the system transition and the reward function to be constant over time. However, the stationarity assumption is restrictive in practice and is likely to be violated in a number of applications, including traffic signal control, robotics and mobile health. In this paper, we develop a consistent procedure to test the nonstationarity of the optimal Q-function based on pre-collected historical data, without additional online data collection. Based on the proposed test, we further develop a sequential change point detection method that can be naturally coupled with existing state-of-the-art RL methods for policy optimization in nonstationary environments. The usefulness of our method is illustrated by theoretical results, simulation studies, and a real data example from the 2018 Intern Health Study. A Python implementation of the proposed procedure is available at https://github.com/limengbinggz/CUSUM-RL.

As machine learning models evolve, maintaining transparency demands more human-centric explainable AI techniques. Counterfactual explanations, with roots in human reasoning, identify the minimal input changes needed to obtain a given output and, hence, are crucial for supporting decision-making. Despite their importance, the evaluation of these explanations often lacks grounding in user studies and remains fragmented, with existing metrics not fully capturing human perspectives. To address this challenge, we developed a diverse set of 30 counterfactual scenarios and collected ratings across 8 evaluation metrics from 206 respondents. Subsequently, we fine-tuned different Large Language Models (LLMs) to predict average or individual human judgment across these metrics. Our methodology allowed LLMs to achieve an accuracy of up to 63% in zero-shot evaluations and 85% (over a 3-classes prediction) with fine-tuning across all metrics. The fine-tuned models predicting human ratings offer better comparability and scalability in evaluating different counterfactual explanation frameworks.

Robust reinforcement learning is essential for deploying reinforcement learning algorithms in real-world scenarios where environmental uncertainty predominates. Traditional robust reinforcement learning often depends on rectangularity assumptions, where adverse probability measures of outcome states are assumed to be independent across different states and actions. This assumption, rarely fulfilled in practice, leads to overly conservative policies. To address this problem, we introduce a new time-constrained robust MDP (TC-RMDP) formulation that considers multifactorial, correlated, and time-dependent disturbances, thus more accurately reflecting real-world dynamics. This formulation goes beyond the conventional rectangularity paradigm, offering new perspectives and expanding the analytical framework for robust RL. We propose three distinct algorithms, each using varying levels of environmental information, and evaluate them extensively on continuous control benchmarks. Our results demonstrate that these algorithms yield an efficient tradeoff between performance and robustness, outperforming traditional deep robust RL methods in time-constrained environments while preserving robustness in classical benchmarks. This study revisits the prevailing assumptions in robust RL and opens new avenues for developing more practical and realistic RL applications.

Reward specification plays a central role in reinforcement learning (RL), guiding the agent's behavior. To express non-Markovian rewards, formalisms such as reward machines have been introduced to capture dependencies on histories. However, traditional reward machines lack the ability to model precise timing constraints, limiting their use in time-sensitive applications. In this paper, we propose timed reward machines (TRMs), which are an extension of reward machines that incorporate timing constraints into the reward structure. TRMs enable more expressive specifications with tunable reward logic, for example, imposing costs for delays and granting rewards for timely actions. We study model-free RL frameworks (i.e., tabular Q-learning) for learning optimal policies with TRMs under digital and real-time semantics. Our algorithms integrate the TRM into learning via abstractions of timed automata, and employ counterfactual-imagining heuristics that exploit the structure of the TRM to improve the search. Experimentally, we demonstrate that our algorithm learns policies that achieve high rewards while satisfying the timing constraints specified by the TRM on popular RL benchmarks. Moreover, we conduct comparative studies of performance under different TRM semantics, along with ablations that highlight the benefits of counterfactual-imagining.

The vast majority of Reinforcement Learning methods is largely impacted by the computation effort and data requirements needed to obtain effective estimates of action-value functions, which in turn determine the quality of the overall performance and the sample-efficiency of the learning procedure. Typically, action-value functions are estimated through an iterative scheme that alternates the application of an empirical approximation of the Bellman operator and a subsequent projection step onto a considered function space. It has been observed that this scheme can be potentially generalized to carry out multiple iterations of the Bellman operator at once, benefiting the underlying learning algorithm. However, till now, it has been challenging to effectively implement this idea, especially in high-dimensional problems. In this paper, we introduce iterated Q-Network (i-QN), a novel principled approach that enables multiple consecutive Bellman updates by learning a tailored sequence of action-value functions where each serves as the target for the next. We show that i-QN is theoretically grounded and that it can be seamlessly used in value-based and actor-critic methods. We empirically demonstrate the advantages of i-QN in Atari 2600 games and MuJoCo continuous control problems.

We propose Q-learning with Adjoint Matching (QAM), a novel TD-based reinforcement learning (RL) algorithm that tackles a long-standing challenge in continuous-action RL: efficient optimization of an expressive diffusion or flow-matching policy with respect to a parameterized Q-function. Effective optimization requires exploiting the first-order information of the critic, but it is challenging to do so for flow or diffusion policies because direct gradient-based optimization via backpropagation through their multi-step denoising process is numerically unstable. Existing methods work around this either by only using the value and discarding the gradient information, or by relying on approximations that sacrifice policy expressivity or bias the learned policy. QAM sidesteps both of these challenges by leveraging adjoint matching, a recently proposed technique in generative modeling, which transforms the critic's action gradient to form a step-wise objective function that is free from unstable backpropagation, while providing an unbiased, expressive policy at the optimum. Combined with temporal-difference backup for critic learning, QAM consistently outperforms prior approaches on hard, sparse reward tasks in both offline and offline-to-online RL.

Large language model (LLM)-based agents have recently shown impressive progress in a variety of domains, including open-ended conversation and multi-step decision-making. However, applying these agents to social deduction games such as Werewolf, which requires both strategic decision-making and free-form language interaction, remains non-trivial. Traditional methods based on Counterfactual Regret Minimization (CFR) or reinforcement learning (RL) typically depend on a predefined action space, making them unsuitable for language games with unconstrained text action space. Meanwhile, pure LLM-based agents often suffer from intrinsic biases and require prohibitively large datasets for fine-tuning. We propose Latent Space Policy Optimization (LSPO), an iterative framework that addresses these challenges by first mapping free-form text to a discrete latent space, where methods like CFR and RL can learn strategic policy more effectively. We then translate the learned policy back into natural language dialogues, which are used to fine-tune an LLM via Direct Preference Optimization (DPO). By iteratively alternating between these stages, our LSPO agent progressively enhances both strategic reasoning and language communication. Experiment results on the Werewolf game show that our method improves the agent's performance in each iteration and outperforms existing Werewolf agents, underscoring its promise for free-form language decision-making.

Offline safe reinforcement learning (RL) seeks reward-maximizing policies from static datasets under strict safety constraints. Existing methods often rely on soft expected-cost objectives or iterative generative inference, which can be insufficient for safety-critical real-time control. We propose Safe Flow Q-Learning (SafeFQL), which extends FQL to safe offline RL by combining a Hamilton--Jacobi reachability-inspired safety value function with an efficient one-step flow policy. SafeFQL learns the safety value via a self-consistency Bellman recursion, trains a flow policy by behavioral cloning, and distills it into a one-step actor for reward-maximizing safe action selection without rejection sampling at deployment. To account for finite-data approximation error in the learned safety boundary, we add a conformal prediction calibration step that adjusts the safety threshold and provides finite-sample probabilistic safety coverage. Empirically, SafeFQL trades modestly higher offline training cost for substantially lower inference latency than diffusion-style safe generative baselines, which is advantageous for real-time safety-critical deployment. Across boat navigation, and Safety Gymnasium MuJoCo tasks, SafeFQL matches or exceeds prior offline safe RL performance while substantially reducing constraint violations.

In real-world scenarios, the application of reinforcement learning is significantly challenged by complex non-stationarity. Most existing methods attempt to model changes in the environment explicitly, often requiring impractical prior knowledge of environments. In this paper, we propose a new perspective, positing that non-stationarity can propagate and accumulate through complex causal relationships during state transitions, thereby compounding its sophistication and affecting policy learning. We believe that this challenge can be more effectively addressed by implicitly tracing the causal origin of non-stationarity. To this end, we introduce the Causal-Origin REPresentation (COREP) algorithm. COREP primarily employs a guided updating mechanism to learn a stable graph representation for the state, termed as causal-origin representation. By leveraging this representation, the learned policy exhibits impressive resilience to non-stationarity. We supplement our approach with a theoretical analysis grounded in the causal interpretation for non-stationary reinforcement learning, advocating for the validity of the causal-origin representation. Experimental results further demonstrate the superior performance of COREP over existing methods in tackling non-stationarity problems.

The fine-tuning of pre-trained large language models (LLMs) using reinforcement learning (RL) is generally formulated as direct policy optimization. This approach was naturally favored as it efficiently improves a pretrained LLM, seen as an initial policy. Another RL paradigm, Q-learning methods, has received far less attention in the LLM community while demonstrating major success in various non-LLM RL tasks. In particular, Q-learning effectiveness comes from its sample efficiency and ability to learn offline, which is particularly valuable given the high computational cost of sampling with LLMs. However, naively applying a Q-learning-style update to the model's logits is ineffective due to the specificity of LLMs. Our core contribution is to derive theoretically grounded loss functions from Bellman equations to adapt Q-learning methods to LLMs. To do so, we carefully adapt insights from the RL literature to account for LLM-specific characteristics, ensuring that the logits become reliable Q-value estimates. We then use this loss to build a practical algorithm, ShiQ for Shifted-Q, that supports off-policy, token-wise learning while remaining simple to implement. Finally, we evaluate ShiQ on both synthetic data and real-world benchmarks, e.g., UltraFeedback and BFCL-V3, demonstrating its effectiveness in both single-turn and multi-turn LLM settings

Risk-averse reinforcement learning finds application in various high-stakes fields. Unlike classical reinforcement learning, which aims to maximize expected returns, risk-averse agents choose policies that minimize risk, occasionally sacrificing expected value. These preferences can be framed through utility theory. We focus on the specific case of the exponential utility function, where we can derive the Bellman equations and employ various reinforcement learning algorithms with few modifications. However, these methods suffer from numerical instability due to the need for exponent computation throughout the process. To address this, we introduce a numerically stable and mathematically sound loss function based on the Itakura-Saito divergence for learning state-value and action-value functions. We evaluate our proposed loss function against established alternatives, both theoretically and empirically. In the experimental section, we explore multiple financial scenarios, some with known analytical solutions, and show that our loss function outperforms the alternatives.

In reinforcement learning (RL), function approximation errors are known to easily lead to the Q-value overestimations, thus greatly reducing policy performance. This paper presents a distributional soft actor-critic (DSAC) algorithm, which is an off-policy RL method for continuous control setting, to improve the policy performance by mitigating Q-value overestimations. We first discover in theory that learning a distribution function of state-action returns can effectively mitigate Q-value overestimations because it is capable of adaptively adjusting the update stepsize of the Q-value function. Then, a distributional soft policy iteration (DSPI) framework is developed by embedding the return distribution function into maximum entropy RL. Finally, we present a deep off-policy actor-critic variant of DSPI, called DSAC, which directly learns a continuous return distribution by keeping the variance of the state-action returns within a reasonable range to address exploding and vanishing gradient problems. We evaluate DSAC on the suite of MuJoCo continuous control tasks, achieving the state-of-the-art performance.

Robustness against adversarial attacks and distribution shifts is a long-standing goal of Reinforcement Learning (RL). To this end, Robust Adversarial Reinforcement Learning (RARL) trains a protagonist against destabilizing forces exercised by an adversary in a competitive zero-sum Markov game, whose optimal solution, i.e., rational strategy, corresponds to a Nash equilibrium. However, finding Nash equilibria requires facing complex saddle point optimization problems, which can be prohibitive to solve, especially for high-dimensional control. In this paper, we propose a novel approach for adversarial RL based on entropy regularization to ease the complexity of the saddle point optimization problem. We show that the solution of this entropy-regularized problem corresponds to a Quantal Response Equilibrium (QRE), a generalization of Nash equilibria that accounts for bounded rationality, i.e., agents sometimes play random actions instead of optimal ones. Crucially, the connection between the entropy-regularized objective and QRE enables free modulation of the rationality of the agents by simply tuning the temperature coefficient. We leverage this insight to propose our novel algorithm, Quantal Adversarial RL (QARL), which gradually increases the rationality of the adversary in a curriculum fashion until it is fully rational, easing the complexity of the optimization problem while retaining robustness. We provide extensive evidence of QARL outperforming RARL and recent baselines across several MuJoCo locomotion and navigation problems in overall performance and robustness.

We consider the task of evaluating policies of algorithmic resource allocation through randomized controlled trials (RCTs). Such policies are tasked with optimizing the utilization of limited intervention resources, with the goal of maximizing the benefits derived. Evaluation of such allocation policies through RCTs proves difficult, notwithstanding the scale of the trial, because the individuals' outcomes are inextricably interlinked through resource constraints controlling the policy decisions. Our key contribution is to present a new estimator leveraging our proposed novel concept, that involves retrospective reshuffling of participants across experimental arms at the end of an RCT. We identify conditions under which such reassignments are permissible and can be leveraged to construct counterfactual trials, whose outcomes can be accurately ascertained, for free. We prove theoretically that such an estimator is more accurate than common estimators based on sample means -- we show that it returns an unbiased estimate and simultaneously reduces variance. We demonstrate the value of our approach through empirical experiments on synthetic, semi-synthetic as well as real case study data and show improved estimation accuracy across the board.

Reinforcement learning (RL) has improved the reasoning abilities of large language models (LLMs), yet state-of-the-art methods still fail to learn on many training problems. On hard problems, on-policy RL rarely explores even a single correct rollout, yielding zero reward and no learning signal for driving improvement. We find that natural solutions to remedy this exploration problem from classical RL, such as entropy bonuses, more permissive clipping of the importance ratio, or direct optimization of pass@k objectives, do not resolve this issue and often destabilize optimization without improving solvability. A natural alternative is to leverage transfer from easier problems. However, we show that mixing easy and hard problems during RL training is counterproductive due to ray interference, where optimization focuses on already-solvable problems in a way that actively inhibits progress on harder ones. To address this challenge, we introduce Privileged On-Policy Exploration (POPE), an approach that leverages human- or other oracle solutions as privileged information to guide exploration on hard problems, unlike methods that use oracle solutions as training targets (e.g., off-policy RL methods or warmstarting from SFT). POPE augments hard problems with prefixes of oracle solutions, enabling RL to obtain non-zero rewards during guided rollouts. Crucially, the resulting behaviors transfer back to the original, unguided problems through a synergy between instruction-following and reasoning. Empirically, POPE expands the set of solvable problems and substantially improves performance on challenging reasoning benchmarks.

Although counterfactual reasoning is a fundamental aspect of intelligence, the lack of large-scale counterfactual open-domain question-answering (QA) benchmarks makes it difficult to evaluate and improve models on this ability. To address this void, we introduce the first such dataset, named IfQA, where each question is based on a counterfactual presupposition via an "if" clause. For example, if Los Angeles was on the east coast of the U.S., what would be the time difference between Los Angeles and Paris? Such questions require models to go beyond retrieving direct factual knowledge from the Web: they must identify the right information to retrieve and reason about an imagined situation that may even go against the facts built into their parameters. The IfQA dataset contains over 3,800 questions that were annotated annotated by crowdworkers on relevant Wikipedia passages. Empirical analysis reveals that the IfQA dataset is highly challenging for existing open-domain QA methods, including supervised retrieve-then-read pipeline methods (EM score 36.2), as well as recent few-shot approaches such as chain-of-thought prompting with GPT-3 (EM score 27.4). The unique challenges posed by the IfQA benchmark will push open-domain QA research on both retrieval and counterfactual reasoning fronts.

We present a general convergent class of reinforcement learning algorithms that is founded on two distinct principles: (1) mapping value estimates to a different space using arbitrary functions from a broad class, and (2) linearly decomposing the reward signal into multiple channels. The first principle enables incorporating specific properties into the value estimator that can enhance learning. The second principle, on the other hand, allows for the value function to be represented as a composition of multiple utility functions. This can be leveraged for various purposes, e.g. dealing with highly varying reward scales, incorporating a priori knowledge about the sources of reward, and ensemble learning. Combining the two principles yields a general blueprint for instantiating convergent algorithms by orchestrating diverse mapping functions over multiple reward channels. This blueprint generalizes and subsumes algorithms such as Q-Learning, Log Q-Learning, and Q-Decomposition. In addition, our convergence proof for this general class relaxes certain required assumptions in some of these algorithms. Based on our theory, we discuss several interesting configurations as special cases. Finally, to illustrate the potential of the design space that our theory opens up, we instantiate a particular algorithm and evaluate its performance on the Atari suite.

In meta reinforcement learning (meta RL), an agent seeks a Bayes-optimal policy -- the optimal policy when facing an unknown task that is sampled from some known task distribution. Previous approaches tackled this problem by inferring a belief over task parameters, using variational inference methods. Motivated by recent successes of contrastive learning approaches in RL, such as contrastive predictive coding (CPC), we investigate whether contrastive methods can be used for learning Bayes-optimal behavior. We begin by proving that representations learned by CPC are indeed sufficient for Bayes optimality. Based on this observation, we propose a simple meta RL algorithm that uses CPC in lieu of variational belief inference. Our method, ContraBAR, achieves comparable performance to state-of-the-art in domains with state-based observation and circumvents the computational toll of future observation reconstruction, enabling learning in domains with image-based observations. It can also be combined with image augmentations for domain randomization and used seamlessly in both online and offline meta RL settings.

Poker, also known as Texas Hold'em, has always been a typical research target within imperfect information games (IIGs). IIGs have long served as a measure of artificial intelligence (AI) development. Representative prior works, such as DeepStack and Libratus heavily rely on counterfactual regret minimization (CFR) to tackle heads-up no-limit Poker. However, it is challenging for subsequent researchers to learn CFR from previous models and apply it to other real-world applications due to the expensive computational cost of CFR iterations. Additionally, CFR is difficult to apply to multi-player games due to the exponential growth of the game tree size. In this work, we introduce PokerGPT, an end-to-end solver for playing Texas Hold'em with arbitrary number of players and gaining high win rates, established on a lightweight large language model (LLM). PokerGPT only requires simple textual information of Poker games for generating decision-making advice, thus guaranteeing the convenient interaction between AI and humans. We mainly transform a set of textual records acquired from real games into prompts, and use them to fine-tune a lightweight pre-trained LLM using reinforcement learning human feedback technique. To improve fine-tuning performance, we conduct prompt engineering on raw data, including filtering useful information, selecting behaviors of players with high win rates, and further processing them into textual instruction using multiple prompt engineering techniques. Through the experiments, we demonstrate that PokerGPT outperforms previous approaches in terms of win rate, model size, training time, and response speed, indicating the great potential of LLMs in solving IIGs.

Vision Language Models (VLMs) have recently shown significant advancements in video understanding, especially in feature alignment, event reasoning, and instruction-following tasks. However, their capability for counterfactual reasoning, inferring alternative outcomes under hypothetical conditions, remains underexplored. This capability is essential for robust video understanding, as it requires identifying underlying causal structures and reasoning about unobserved possibilities, rather than merely recognizing observed patterns. To systematically evaluate this capability, we introduce CounterVQA, a video-based benchmark featuring three progressive difficulty levels that assess different aspects of counterfactual reasoning. Through comprehensive evaluation of both state-of-the-art open-source and closed-source models, we uncover a substantial performance gap: while these models achieve reasonable accuracy on simple counterfactual questions, performance degrades significantly on complex multi-hop causal chains. To address these limitations, we develop a post-training method, CFGPT, that enhances a model's visual counterfactual reasoning ability by distilling its counterfactual reasoning capability from the language modality, yielding consistent improvements across all CounterVQA difficulty levels. Dataset and code will be further released.

This paper studies online nonstochastic control problems with adversarial and static constraints. We propose online nonstochastic control algorithms that achieve both sublinear regret and sublinear adversarial constraint violation while keeping static constraint violation minimal against the optimal constrained linear control policy in hindsight. To establish the results, we introduce an online convex optimization with memory framework under adversarial and static constraints, which serves as a subroutine for the constrained online nonstochastic control algorithms. This subroutine also achieves the state-of-the-art regret and constraint violation bounds for constrained online convex optimization problems, which is of independent interest. Our experiments demonstrate the proposed control algorithms are adaptive to adversarial constraints and achieve smaller cumulative costs and violations. Moreover, our algorithms are less conservative and achieve significantly smaller cumulative costs than the state-of-the-art algorithm.

Recent advances in large reasoning models highlight Reinforcement Learning with Verifiable Rewards (RLVR) as a promising method for enhancing AI's capabilities, particularly in solving complex logical tasks. However, it remains unclear whether RLVR truly expands a model's reasoning boundary or merely amplifies high-reward outputs that the base model already knows for improved precision. This study presents a theoretical and empirical investigation that provides fresh insights into the potential limits of RLVR. First, we offer a new theoretical perspective that RLVR is constrained by the base model's support-unable to sample solutions with zero initial probability-and operates as a conservative reweighting mechanism that may restrict the discovery of entirely original solutions. We also identify an entropy-reward tradeoff: while RLVR reliably enhances precision, it may progressively narrow exploration and potentially overlook correct yet underrepresented solutions. Extensive empirical experiments validate that while RLVR consistently improves pass@1, the shrinkage of empirical support generally outweighs the expansion of empirical support under larger sampling budgets, failing to recover correct answers that were previously accessible to the base model. Interestingly, we also observe that while RLVR sometimes increases token-level entropy, resulting in greater uncertainty at each generation step, answer-level entropy declines, indicating that these seemingly more uncertain paths ultimately converge onto a smaller set of distinct answers. Taken together, these findings reveal potential limits of RLVR in extending reasoning horizons. Breaking this invisible leash may require future algorithmic innovations such as explicit exploration mechanisms or hybrid strategies that seed probability mass into underrepresented solution regions.

We consider the problem of preference based reinforcement learning (PbRL), where, unlike traditional reinforcement learning, an agent receives feedback only in terms of a 1 bit (0/1) preference over a trajectory pair instead of absolute rewards for them. The success of the traditional RL framework crucially relies on the underlying agent-reward model, which, however, depends on how accurately a system designer can express an appropriate reward function and often a non-trivial task. The main novelty of our framework is the ability to learn from preference-based trajectory feedback that eliminates the need to hand-craft numeric reward models. This paper sets up a formal framework for the PbRL problem with non-markovian rewards, where the trajectory preferences are encoded by a generalized linear model of dimension d. Assuming the transition model is known, we then propose an algorithm with almost optimal regret guarantee of mathcal{O}left( SH d log (T / delta) T right). We further, extend the above algorithm to the case of unknown transition dynamics, and provide an algorithm with near optimal regret guarantee mathcal{O}((d + H^2 + |S|)dT +|mathcal{S||A|TH} ). To the best of our knowledge, our work is one of the first to give tight regret guarantees for preference based RL problems with trajectory preferences.

Existing Large Language Model (LLM) agents struggle in interactive environments requiring long-horizon planning, primarily due to compounding errors when simulating future states. To address this, we propose ProAct, a framework that enables agents to internalize accurate lookahead reasoning through a two-stage training paradigm. First, we introduce Grounded LookAhead Distillation (GLAD), where the agent undergoes supervised fine-tuning on trajectories derived from environment-based search. By compressing complex search trees into concise, causal reasoning chains, the agent learns the logic of foresight without the computational overhead of inference-time search. Second, to further refine decision accuracy, we propose the Monte-Carlo Critic (MC-Critic), a plug-and-play auxiliary value estimator designed to enhance policy-gradient algorithms like PPO and GRPO. By leveraging lightweight environment rollouts to calibrate value estimates, MC-Critic provides a low-variance signal that facilitates stable policy optimization without relying on expensive model-based value approximation. Experiments on both stochastic (e.g., 2048) and deterministic (e.g., Sokoban) environments demonstrate that ProAct significantly improves planning accuracy. Notably, a 4B parameter model trained with ProAct outperforms all open-source baselines and rivals state-of-the-art closed-source models, while demonstrating robust generalization to unseen environments. The codes and models are available at https://github.com/GreatX3/ProAct

Recent advances in multimodal language models (MLLMs) have achieved remarkable progress in vision-language reasoning, especially with the emergence of "thinking with images," which integrates explicit visual steps into the reasoning process. While this paradigm strengthens image-based reasoning, a significant challenge remains: models may arrive at correct answers by relying on irrelevant or spurious regions, driven by prior knowledge or dataset biases. Even when the answer is correct, flawed reasoning indicates that the model has not truly understood the image, highlighting the critical importance of reasoning fidelity in multimodal tasks. To address this issue, we propose DeFacto, a counterfactual reasoning framework that jointly enforces accurate answering and faithful reasoning. A key component of our approach is the design of three complementary training paradigms: (i) positive, (ii) counterfactual, and (iii) random-masking. To enable these paradigms, we develop a pipeline that automatically localizes question-relevant evidence and constructs positive, counterfactual, and random variants, resulting in a dataset of about 100k images. Building on this framework, we train multimodal language models with GRPO-based reinforcement learning, where we design three complementary rewards to guide the model toward accurate answering and evidence-grounded reasoning. Experiments on diverse benchmarks demonstrate that DeFacto substantially improves both answer accuracy and reasoning faithfulness, establishing a stronger foundation for interpretable multimodal reasoning. The code is available on GitHub and the dataset is released on HuggingFace.

Planning safe robot motions in the presence of humans requires reliable forecasts of future human motion. However, simply predicting the most likely motion from prior interactions does not guarantee safety. Such forecasts fail to model the long tail of possible events, which are rarely observed in limited datasets. On the other hand, planning for worst-case motions leads to overtly conservative behavior and a "frozen robot". Instead, we aim to learn forecasts that predict counterfactuals that humans guard against. We propose a novel game-theoretic framework for joint planning and forecasting with the payoff being the performance of the planner against the demonstrator, and present practical algorithms to train models in an end-to-end fashion. We demonstrate that our proposed algorithm results in safer plans in a crowd navigation simulator and real-world datasets of pedestrian motion. We release our code at https://github.com/portal-cornell/Game-Theoretic-Forecasting-Planning.

We investigate learning the equilibria in non-stationary multi-agent systems and address the challenges that differentiate multi-agent learning from single-agent learning. Specifically, we focus on games with bandit feedback, where testing an equilibrium can result in substantial regret even when the gap to be tested is small, and the existence of multiple optimal solutions (equilibria) in stationary games poses extra challenges. To overcome these obstacles, we propose a versatile black-box approach applicable to a broad spectrum of problems, such as general-sum games, potential games, and Markov games, when equipped with appropriate learning and testing oracles for stationary environments. Our algorithms can achieve Oleft(Delta^{1/4}T^{3/4}right) regret when the degree of nonstationarity, as measured by total variation Delta, is known, and Oleft(Delta^{1/5}T^{4/5}right) regret when Delta is unknown, where T is the number of rounds. Meanwhile, our algorithm inherits the favorable dependence on number of agents from the oracles. As a side contribution that may be independent of interest, we show how to test for various types of equilibria by a black-box reduction to single-agent learning, which includes Nash equilibria, correlated equilibria, and coarse correlated equilibria.

We consider the problem of learning the best possible policy from a fixed dataset, known as offline Reinforcement Learning (RL). A common taxonomy of existing offline RL works is policy regularization, which typically constrains the learned policy by distribution or support of the behavior policy. However, distribution and support constraints are overly conservative since they both force the policy to choose similar actions as the behavior policy when considering particular states. It will limit the learned policy's performance, especially when the behavior policy is sub-optimal. In this paper, we find that regularizing the policy towards the nearest state-action pair can be more effective and thus propose Policy Regularization with Dataset Constraint (PRDC). When updating the policy in a given state, PRDC searches the entire dataset for the nearest state-action sample and then restricts the policy with the action of this sample. Unlike previous works, PRDC can guide the policy with proper behaviors from the dataset, allowing it to choose actions that do not appear in the dataset along with the given state. It is a softer constraint but still keeps enough conservatism from out-of-distribution actions. Empirical evidence and theoretical analysis show that PRDC can alleviate offline RL's fundamentally challenging value overestimation issue with a bounded performance gap. Moreover, on a set of locomotion and navigation tasks, PRDC achieves state-of-the-art performance compared with existing methods. Code is available at https://github.com/LAMDA-RL/PRDC

The popular Q-learning algorithm is known to overestimate action values under certain conditions. It was not previously known whether, in practice, such overestimations are common, whether they harm performance, and whether they can generally be prevented. In this paper, we answer all these questions affirmatively. In particular, we first show that the recent DQN algorithm, which combines Q-learning with a deep neural network, suffers from substantial overestimations in some games in the Atari 2600 domain. We then show that the idea behind the Double Q-learning algorithm, which was introduced in a tabular setting, can be generalized to work with large-scale function approximation. We propose a specific adaptation to the DQN algorithm and show that the resulting algorithm not only reduces the observed overestimations, as hypothesized, but that this also leads to much better performance on several games.

Fair decisions require ignoring irrelevant, potentially biasing, information. To achieve this, decision-makers need to approximate what decision they would have made had they not known certain facts, such as the gender or race of a job candidate. This counterfactual self-simulation is notoriously hard for humans, leading to biased judgments even by well-meaning actors. Here we show that large language models (LLMs) suffer from similar limitations in their ability to approximate what decisions they would make under counterfactual knowledge in offsetting gender and race biases and overcoming sycophancy. We show that prompting models to ignore or pretend not to know biasing information fails to offset these biases and occasionally backfires. However, unlike humans, LLMs can be given access to a ground-truth model of their own counterfactual cognition -- their own API. We show that this access to the responses of a blinded replica enables fairer decisions, while providing greater transparency to distinguish implicit from intentionally biased behavior.

Recently, it has been shown that for offline deep reinforcement learning (DRL), pre-training Decision Transformer with a large language corpus can improve downstream performance (Reid et al., 2022). A natural question to ask is whether this performance gain can only be achieved with language pre-training, or can be achieved with simpler pre-training schemes which do not involve language. In this paper, we first show that language is not essential for improved performance, and indeed pre-training with synthetic IID data for a small number of updates can match the performance gains from pre-training with a large language corpus; moreover, pre-training with data generated by a one-step Markov chain can further improve the performance. Inspired by these experimental results, we then consider pre-training Conservative Q-Learning (CQL), a popular offline DRL algorithm, which is Q-learning-based and typically employs a Multi-Layer Perceptron (MLP) backbone. Surprisingly, pre-training with simple synthetic data for a small number of updates can also improve CQL, providing consistent performance improvement on D4RL Gym locomotion datasets. The results of this paper not only illustrate the importance of pre-training for offline DRL but also show that the pre-training data can be synthetic and generated with remarkably simple mechanisms.

Probabilistic dynamics model ensemble is widely used in existing model-based reinforcement learning methods as it outperforms a single dynamics model in both asymptotic performance and sample efficiency. In this paper, we provide both practical and theoretical insights on the empirical success of the probabilistic dynamics model ensemble through the lens of Lipschitz continuity. We find that, for a value function, the stronger the Lipschitz condition is, the smaller the gap between the true dynamics- and learned dynamics-induced Bellman operators is, thus enabling the converged value function to be closer to the optimal value function. Hence, we hypothesize that the key functionality of the probabilistic dynamics model ensemble is to regularize the Lipschitz condition of the value function using generated samples. To test this hypothesis, we devise two practical robust training mechanisms through computing the adversarial noise and regularizing the value network's spectral norm to directly regularize the Lipschitz condition of the value functions. Empirical results show that combined with our mechanisms, model-based RL algorithms with a single dynamics model outperform those with an ensemble of probabilistic dynamics models. These findings not only support the theoretical insight, but also provide a practical solution for developing computationally efficient model-based RL algorithms.

Reinforcement learning (RL) tasks are typically framed as Markov Decision Processes (MDPs), assuming that decisions are made at fixed time intervals. However, many applications of great importance, including healthcare, do not satisfy this assumption, yet they are commonly modelled as MDPs after an artificial reshaping of the data. In addition, most healthcare (and similar) problems are offline by nature, allowing for only retrospective studies. To address both challenges, we begin by discussing the Semi-MDP (SMDP) framework, which formally handles actions of variable timings. We next present a formal way to apply SMDP modifications to nearly any given value-based offline RL method. We use this theory to introduce three SMDP-based offline RL algorithms, namely, SDQN, SDDQN, and SBCQ. We then experimentally demonstrate that only these SMDP-based algorithms learn the optimal policy in variable-time environments, whereas their MDP counterparts do not. Finally, we apply our new algorithms to a real-world offline dataset pertaining to warfarin dosing for stroke prevention and demonstrate similar results.

Group-Relative Policy Optimization (GRPO) is a key technique for training large reasoning models, yet it suffers from a critical vulnerability: the Think-Answer Mismatch, where noisy reward signals corrupt the learning process. This problem is most severe in unbalanced response groups, paradoxically degrading the signal precisely when it should be most informative. To address this challenge, we propose Stable Group-Relative Policy Optimization (S-GRPO), a principled enhancement that derives optimal, noise-aware advantage weights to stabilize training. Our comprehensive experiments on mathematical reasoning benchmarks demonstrate S-GRPO's effectiveness and robustness. On various models, S-GRPO significantly outperforms DR. GRPO, achieving performance gains of +2.5% on Qwen-Math-7B-Base, +2.2% on Llama-3.2-3B-Base, and +2.4% on Qwen-Math-1.5B-Instruct. Most critically, while standard GRPO fails to learn under 20% synthetic reward noise, S-GRPO maintains stable learning progress. These results highlight S-GRPO's potential for more robust and effective training of large-scale reasoning models. \footnote{Code and data are available at: https://github.com/shenpeijun0212/S-GRPO

Concept-based explanations quantify how high-level concepts (e.g., gender or experience) influence model behavior, which is crucial for decision-makers in high-stakes domains. Recent work evaluates the faithfulness of such explanations by comparing them to reference causal effects estimated from counterfactuals. In practice, existing benchmarks rely on costly human-written counterfactuals that serve as an imperfect proxy. To address this, we introduce a framework for constructing datasets containing structural counterfactual pairs: LIBERTy (LLM-based Interventional Benchmark for Explainability with Reference Targets). LIBERTy is grounded in explicitly defined Structured Causal Models (SCMs) of the text generation, interventions on a concept propagate through the SCM until an LLM generates the counterfactual. We introduce three datasets (disease detection, CV screening, and workplace violence prediction) together with a new evaluation metric, order-faithfulness. Using them, we evaluate a wide range of methods across five models and identify substantial headroom for improving concept-based explanations. LIBERTy also enables systematic analysis of model sensitivity to interventions: we find that proprietary LLMs show markedly reduced sensitivity to demographic concepts, likely due to post-training mitigation. Overall, LIBERTy provides a much-needed benchmark for developing faithful explainability methods.

Off-policy reinforcement learning (RL) has proven to be a powerful framework for guiding agents' actions in environments with stochastic rewards and unknown or noisy state dynamics. In many real-world settings, these agents must operate in multiple environments, each with slightly different dynamics. For example, we may be interested in developing policies to guide medical treatment for patients with and without a given disease, or policies to navigate curriculum design for students with and without a learning disability. Here, we introduce nested policy fitted Q-iteration (NFQI), an RL framework that finds optimal policies in environments that exhibit such a structure. Our approach develops a nested Q-value function that takes advantage of the shared structure between two groups of observations from two separate environments while allowing their policies to be distinct from one another. We find that NFQI yields policies that rely on relevant features and perform at least as well as a policy that does not consider group structure. We demonstrate NFQI's performance using an OpenAI Gym environment and a clinical decision making RL task. Our results suggest that NFQI can develop policies that are better suited to many real-world clinical environments.

In this paper, we investigate the problem of offline Preference-based Reinforcement Learning (PbRL) with human feedback where feedback is available in the form of preference between trajectory pairs rather than explicit rewards. Our proposed algorithm consists of two main steps: (1) estimate the implicit reward using Maximum Likelihood Estimation (MLE) with general function approximation from offline data and (2) solve a distributionally robust planning problem over a confidence set around the MLE. We consider the general reward setting where the reward can be defined over the whole trajectory and provide a novel guarantee that allows us to learn any target policy with a polynomial number of samples, as long as the target policy is covered by the offline data. This guarantee is the first of its kind with general function approximation. To measure the coverage of the target policy, we introduce a new single-policy concentrability coefficient, which can be upper bounded by the per-trajectory concentrability coefficient. We also establish lower bounds that highlight the necessity of such concentrability and the difference from standard RL, where state-action-wise rewards are directly observed. We further extend and analyze our algorithm when the feedback is given over action pairs.

We study how a central bank should dynamically set short-term nominal interest rates to stabilize inflation and unemployment when macroeconomic relationships are uncertain and time-varying. We model monetary policy as a sequential decision-making problem where the central bank observes macroeconomic conditions quarterly and chooses interest rate adjustments. Using publically accessible historical Federal Reserve Economic Data (FRED), we construct a linear-Gaussian transition model and implement a discrete-action Markov Decision Process with a quadratic loss reward function. We chose to compare nine different reinforcement learning style approaches against Taylor Rule and naive baselines, including tabular Q-learning variants, SARSA, Actor-Critic, Deep Q-Networks, Bayesian Q-learning with uncertainty quantification, and POMDP formulations with partial observability. Surprisingly, standard tabular Q-learning achieved the best performance (-615.13 +- 309.58 mean return), outperforming both enhanced RL methods and traditional policy rules. Our results suggest that while sophisticated RL techniques show promise for monetary policy applications, simpler approaches may be more robust in this domain, highlighting important challenges in applying modern RL to macroeconomic policy.

Reinforcement Learning with Verifiable Rewards (RLVR) strengthens LLM reasoning, but training often oscillates between {entropy collapse} and {entropy explosion}. We trace both hazards to the mean baseline used in value-free RL (e.g., GRPO and DAPO), which improperly penalizes negative-advantage samples under reward outliers. We propose {Quantile Advantage Estimation} (QAE), replacing the mean with a group-wise K-quantile baseline. QAE induces a response-level, two-regime gate: on hard queries (p <= 1 - K) it reinforces rare successes, while on easy queries (p > 1 - K) it targets remaining failures. Under first-order softmax updates, we prove {two-sided entropy safety}, giving lower and upper bounds on one-step entropy change that curb explosion and prevent collapse. Empirically, this minimal modification stabilizes entropy, sparsifies credit assignment (with tuned K, roughly 80% of responses receive zero advantage), and yields sustained pass@1 gains on Qwen3-8B/14B-Base across AIME 2024/2025 and AMC 2023. These results identify {baseline design} -- rather than token-level heuristics -- as the primary mechanism for scaling RLVR.

Offline reinforcement learning (RL) allows agents to learn effective, return-maximizing policies from a static dataset. Three popular algorithms for offline RL are Conservative Q-Learning (CQL), Behavior Cloning (BC), and Decision Transformer (DT), from the class of Q-Learning, Imitation Learning, and Sequence Modeling respectively. A key open question is: which algorithm is preferred under what conditions? We study this question empirically by exploring the performance of these algorithms across the commonly used D4RL and Robomimic benchmarks. We design targeted experiments to understand their behavior concerning data suboptimality, task complexity, and stochasticity. Our key findings are: (1) DT requires more data than CQL to learn competitive policies but is more robust; (2) DT is a substantially better choice than both CQL and BC in sparse-reward and low-quality data settings; (3) DT and BC are preferable as task horizon increases, or when data is obtained from human demonstrators; and (4) CQL excels in situations characterized by the combination of high stochasticity and low data quality. We also investigate architectural choices and scaling trends for DT on Atari and D4RL and make design/scaling recommendations. We find that scaling the amount of data for DT by 5x gives a 2.5x average score improvement on Atari.

We present counterfactual planning as a design approach for creating a range of safety mechanisms that can be applied in hypothetical future AI systems which have Artificial General Intelligence. The key step in counterfactual planning is to use an AGI machine learning system to construct a counterfactual world model, designed to be different from the real world the system is in. A counterfactual planning agent determines the action that best maximizes expected utility in this counterfactual planning world, and then performs the same action in the real world. We use counterfactual planning to construct an AGI agent emergency stop button, and a safety interlock that will automatically stop the agent before it undergoes an intelligence explosion. We also construct an agent with an input terminal that can be used by humans to iteratively improve the agent's reward function, where the incentive for the agent to manipulate this improvement process is suppressed. As an example of counterfactual planning in a non-agent AGI system, we construct a counterfactual oracle. As a design approach, counterfactual planning is built around the use of a graphical notation for defining mathematical counterfactuals. This two-diagram notation also provides a compact and readable language for reasoning about the complex types of self-referencing and indirect representation which are typically present inside machine learning agents.

Offline reinforcement learning requires reconciling two conflicting aims: learning a policy that improves over the behavior policy that collected the dataset, while at the same time minimizing the deviation from the behavior policy so as to avoid errors due to distributional shift. This trade-off is critical, because most current offline reinforcement learning methods need to query the value of unseen actions during training to improve the policy, and therefore need to either constrain these actions to be in-distribution, or else regularize their values. We propose an offline RL method that never needs to evaluate actions outside of the dataset, but still enables the learned policy to improve substantially over the best behavior in the data through generalization. The main insight in our work is that, instead of evaluating unseen actions from the latest policy, we can approximate the policy improvement step implicitly by treating the state value function as a random variable, with randomness determined by the action (while still integrating over the dynamics to avoid excessive optimism), and then taking a state conditional upper expectile of this random variable to estimate the value of the best actions in that state. This leverages the generalization capacity of the function approximator to estimate the value of the best available action at a given state without ever directly querying a Q-function with this unseen action. Our algorithm alternates between fitting this upper expectile value function and backing it up into a Q-function. Then, we extract the policy via advantage-weighted behavioral cloning. We dub our method implicit Q-learning (IQL). IQL demonstrates the state-of-the-art performance on D4RL, a standard benchmark for offline reinforcement learning. We also demonstrate that IQL achieves strong performance fine-tuning using online interaction after offline initialization.

To address the interpretability challenge in machine learning (ML) systems, counterfactual explanations (CEs) have emerged as a promising solution. CEs are unique as they provide workable suggestions to users, in addition to explaining why a certain outcome was predicted. The application of CEs encounters two main challenges: general user preferences and variable ML systems. User preferences tend to be general rather than specific, and CEs need to be adaptable to variable ML models while maintaining robustness even as these models change. Facing these challenges, we present a solution rooted in validated general user preferences, which are derived from thorough user research. We map these preferences to the properties of CEs. Additionally, we introduce a novel method, Tree-based Conditions Optional Links (T-COL), which incorporates two optional structures and multiple condition groups for generating CEs adaptable to general user preferences. Meanwhile, we employ T-COL to enhance the robustness of CEs with specific conditions, making them more valid even when the ML model is replaced. Our experimental comparisons under different user preferences show that T-COL outperforms all baselines, including Large Language Models which are shown to be able to generate counterfactuals.

Large Reasoning Models (LRMs) have significantly enhanced their capabilities in complex problem-solving by introducing a thinking draft that enables multi-path Chain-of-Thought explorations before producing final answers. Ensuring the faithfulness of these intermediate reasoning processes is crucial for reliable monitoring, interpretation, and effective control. In this paper, we propose a systematic counterfactual intervention framework to rigorously evaluate thinking draft faithfulness. Our approach focuses on two complementary dimensions: (1) Intra-Draft Faithfulness, which assesses whether individual reasoning steps causally influence subsequent steps and the final draft conclusion through counterfactual step insertions; and (2) Draft-to-Answer Faithfulness, which evaluates whether final answers are logically consistent with and dependent on the thinking draft, by perturbing the draft's concluding logic. We conduct extensive experiments across six state-of-the-art LRMs. Our findings show that current LRMs demonstrate selective faithfulness to intermediate reasoning steps and frequently fail to faithfully align with the draft conclusions. These results underscore the need for more faithful and interpretable reasoning in advanced LRMs.

Existing Score-Based Models (SBMs) can be categorized into constrained SBMs (CSBMs) or unconstrained SBMs (USBMs) according to their parameterization approaches. CSBMs model probability density functions as Boltzmann distributions, and assign their predictions as the negative gradients of some scalar-valued energy functions. On the other hand, USBMs employ flexible architectures capable of directly estimating scores without the need to explicitly model energy functions. In this paper, we demonstrate that the architectural constraints of CSBMs may limit their modeling ability. In addition, we show that USBMs' inability to preserve the property of conservativeness may lead to degraded performance in practice. To address the above issues, we propose Quasi-Conservative Score-Based Models (QCSBMs) for keeping the advantages of both CSBMs and USBMs. Our theoretical derivations demonstrate that the training objective of QCSBMs can be efficiently integrated into the training processes by leveraging the Hutchinson's trace estimator. In addition, our experimental results on the CIFAR-10, CIFAR-100, ImageNet, and SVHN datasets validate the effectiveness of QCSBMs. Finally, we justify the advantage of QCSBMs using an example of a one-layered autoencoder.

Recent advances in applying reinforcement learning (RL) to large language models (LLMs) have led to substantial progress. In particular, a series of remarkable yet often counterintuitive phenomena have been reported in LLMs, exhibiting patterns not typically observed in traditional RL settings. For example, notable claims include that a single training example can match the performance achieved with an entire dataset, that the reward signal does not need to be very accurate, and that training solely with negative samples can match or even surpass sophisticated reward-based methods. However, the precise conditions under which these observations hold - and, critically, when they fail - remain unclear. In this work, we identify a key factor that differentiates RL observations: whether the pretrained model already exhibits strong Model-Task Alignment, as measured by pass@k accuracy on the evaluated task. Through a systematic and comprehensive examination of a series of counterintuitive claims, supported by rigorous experimental validation across different model architectures and task domains, our findings show that while standard RL training remains consistently robust across settings, many of these counterintuitive results arise only when the model and task already exhibit strong model-task alignment. In contrast, these techniques fail to drive substantial learning in more challenging regimes, where standard RL methods remain effective.

In this paper, we study offline Reinforcement Learning with Human Feedback (RLHF) where we aim to learn the human's underlying reward and the MDP's optimal policy from a set of trajectories induced by human choices. RLHF is challenging for multiple reasons: large state space but limited human feedback, the bounded rationality of human decisions, and the off-policy distribution shift. In this paper, we focus on the Dynamic Discrete Choice (DDC) model for modeling and understanding human choices. DCC, rooted in econometrics and decision theory, is widely used to model a human decision-making process with forward-looking and bounded rationality. We propose a Dynamic-Choice-Pessimistic-Policy-Optimization (DCPPO) method. \ The method involves a three-stage process: The first step is to estimate the human behavior policy and the state-action value function via maximum likelihood estimation (MLE); the second step recovers the human reward function via minimizing Bellman mean squared error using the learned value functions; the third step is to plug in the learned reward and invoke pessimistic value iteration for finding a near-optimal policy. With only single-policy coverage (i.e., optimal policy) of the dataset, we prove that the suboptimality of DCPPO almost matches the classical pessimistic offline RL algorithm in terms of suboptimality's dependency on distribution shift and dimension. To the best of our knowledge, this paper presents the first theoretical guarantees for off-policy offline RLHF with dynamic discrete choice model.

Learning to play optimally against any mixture over a diverse set of strategies is of important practical interests in competitive games. In this paper, we propose simplex-NeuPL that satisfies two desiderata simultaneously: i) learning a population of strategically diverse basis policies, represented by a single conditional network; ii) using the same network, learn best-responses to any mixture over the simplex of basis policies. We show that the resulting conditional policies incorporate prior information about their opponents effectively, enabling near optimal returns against arbitrary mixture policies in a game with tractable best-responses. We verify that such policies behave Bayes-optimally under uncertainty and offer insights in using this flexibility at test time. Finally, we offer evidence that learning best-responses to any mixture policies is an effective auxiliary task for strategic exploration, which, by itself, can lead to more performant populations.

Training reinforcement learning (RL) systems in real-world environments remains challenging due to noisy supervision and poor out-of-domain (OOD) generalization, especially in LLM post-training. Recent distributional RL methods improve robustness by modeling values with multiple quantile points, but they still learn each quantile independently as a scalar. This results in rough-grained value representations that lack fine-grained conditioning on state information, struggling under complex and OOD conditions. We propose DFPO (Distributional Value Flow Policy Optimization with Conditional Risk and Consistency Control), a robust distributional RL framework that models values as continuous flows across time steps. By scaling value modeling through learning of a value flow field instead of isolated quantile predictions, DFPO captures richer state information for more accurate advantage estimation. To stabilize training under noisy feedback, DFPO further integrates conditional risk control and consistency constraints along value flow trajectories. Experiments on dialogue, math reasoning, and scientific tasks show that DFPO outperforms PPO, FlowRL, and other robust baselines under noisy supervision, achieving improved training stability and generalization.

While originally developed for continuous control problems, Proximal Policy Optimization (PPO) has emerged as the work-horse of a variety of reinforcement learning (RL) applications including the fine-tuning of generative models. Unfortunately, PPO requires multiple heuristics to enable stable convergence (e.g. value networks, clipping) and is notorious for its sensitivity to the precise implementation of these components. In response, we take a step back and ask what a minimalist RL algorithm for the era of generative models would look like. We propose REBEL, an algorithm that cleanly reduces the problem of policy optimization to regressing the relative rewards via a direct policy parameterization between two completions to a prompt, enabling strikingly lightweight implementation. In theory, we prove that fundamental RL algorithms like Natural Policy Gradient can be seen as variants of REBEL, which allows us to match the strongest known theoretical guarantees in terms of convergence and sample complexity in the RL literature. REBEL can also cleanly incorporate offline data and handle the intransitive preferences we frequently see in practice. Empirically, we find that REBEL provides a unified approach to language modeling and image generation with stronger or similar performance as PPO and DPO, all while being simpler to implement and more computationally tractable than PPO.

When reward functions are hand-designed, deep reinforcement learning algorithms often suffer from reward misspecification, causing them to learn suboptimal policies in terms of the intended task objectives. In the single-agent case, inverse reinforcement learning (IRL) techniques attempt to address this issue by inferring the reward function from expert demonstrations. However, in multi-agent problems, misalignment between the learned and true objectives is exacerbated due to increased environment non-stationarity and variance that scales with multiple agents. As such, in multi-agent general-sum games, multi-agent IRL algorithms have difficulty balancing cooperative and competitive objectives. To address these issues, we propose Multi-Agent Marginal Q-Learning from Demonstrations (MAMQL), a novel sample-efficient framework for multi-agent IRL. For each agent, MAMQL learns a critic marginalized over the other agents' policies, allowing for a well-motivated use of Boltzmann policies in the multi-agent context. We identify a connection between optimal marginalized critics and single-agent soft-Q IRL, allowing us to apply a direct, simple optimization criterion from the single-agent domain. Across our experiments on three different simulated domains, MAMQL significantly outperforms previous multi-agent methods in average reward, sample efficiency, and reward recovery by often more than 2-5x. We make our code available at https://sites.google.com/view/mamql .

In practical reinforcement learning (RL), the discount factor used for estimating value functions often differs from that used for defining the evaluation objective. In this work, we study the effect that this discrepancy of discount factors has during learning, and discover a family of objectives that interpolate value functions of two distinct discount factors. Our analysis suggests new ways for estimating value functions and performing policy optimization updates, which demonstrate empirical performance gains. This framework also leads to new insights on commonly-used deep RL heuristic modifications to policy optimization algorithms.

We study the adaption of Soft Actor-Critic (SAC), which is considered as a state-of-the-art reinforcement learning (RL) algorithm, from continuous action space to discrete action space. We revisit vanilla discrete SAC and provide an in-depth understanding of its Q value underestimation and performance instability issues when applied to discrete settings. We thereby propose Stable Discrete SAC (SDSAC), an algorithm that leverages entropy-penalty and double average Q-learning with Q-clip to address these issues. Extensive experiments on typical benchmarks with discrete action space, including Atari games and a large-scale MOBA game, show the efficacy of our proposed method. Our code is at: https://github.com/coldsummerday/SD-SAC.git.

We study offline multi-agent reinforcement learning (RL) in Markov games, where the goal is to learn an approximate equilibrium -- such as Nash equilibrium and (Coarse) Correlated Equilibrium -- from an offline dataset pre-collected from the game. Existing works consider relatively restricted tabular or linear models and handle each equilibria separately. In this work, we provide the first framework for sample-efficient offline learning in Markov games under general function approximation, handling all 3 equilibria in a unified manner. By using Bellman-consistent pessimism, we obtain interval estimation for policies' returns, and use both the upper and the lower bounds to obtain a relaxation on the gap of a candidate policy, which becomes our optimization objective. Our results generalize prior works and provide several additional insights. Importantly, we require a data coverage condition that improves over the recently proposed "unilateral concentrability". Our condition allows selective coverage of deviation policies that optimally trade-off between their greediness (as approximate best responses) and coverage, and we show scenarios where this leads to significantly better guarantees. As a new connection, we also show how our algorithmic framework can subsume seemingly different solution concepts designed for the special case of two-player zero-sum games.

Offline goal-conditioned reinforcement learning (GCRL) learns goal-conditioned policies from static pre-collected datasets. However, accurate value estimation remains a challenge due to the limited coverage of the state-action space. Recent physics-informed approaches have sought to address this by imposing physical and geometric constraints on the value function through regularization defined over first-order partial differential equations (PDEs), such as the Eikonal equation. However, these formulations can often be ill-posed in complex, high-dimensional environments. In this work, we propose a physics-informed regularization derived from the viscosity solution of the Hamilton-Jacobi-Bellman (HJB) equation. By providing a physics-based inductive bias, our approach grounds the learning process in optimal control theory, explicitly regularizing and bounding updates during value iterations. Furthermore, we leverage the Feynman-Kac theorem to recast the PDE solution as an expectation, enabling a tractable Monte Carlo estimation of the objective that avoids numerical instability in higher-order gradients. Experiments demonstrate that our method improves geometric consistency, making it broadly applicable to navigation and high-dimensional, complex manipulation tasks. Open-source codes are available at https://github.com/HrishikeshVish/phys-fk-value-GCRL.

Reinforcement learning has become a cornerstone technique for developing reasoning models in complex tasks, ranging from mathematical problem-solving to imaginary reasoning. The optimization of these models typically relies on policy gradient methods, whose efficacy hinges on the accurate estimation of an advantage function. However, prevailing methods typically employ static advantage estimation, a practice that leads to inefficient credit assignment by neglecting the dynamic utility of training samples over time. This limitation results in suboptimal policy updates, which in turn manifest as slower convergence rates and increased learning instability, as models fail to adapt to evolving sample utilities effectively. To address this problem, we introduce ADORA (Advantage Dynamics via Online Rollout Adaptation), a novel framework for policy optimization. ADORA dynamically adjusts the advantage function's weighting by adaptively categorizing training data into temporarily advantageous and disadvantageous samples, based on their evolving utility during online model rollouts. This tailored data differentiation strategy allows ADORA to be seamlessly integrated into existing policy optimization algorithms without significant architectural modifications, enabling the policy to prioritize learning from more informative experiences and thereby achieve more efficient policy updates. Extensive evaluations across diverse model families and varying data scales demonstrate that ADORA is a robust and efficient framework. It significantly enhances long reasoning in both geometric and mathematical tasks, consistently achieving notable performance gains without requiring sensitive hyperparameter tuning.

We study the problem of nonepisodic reinforcement learning (RL) for nonlinear dynamical systems, where the system dynamics are unknown and the RL agent has to learn from a single trajectory, i.e., without resets. We propose Nonepisodic Optimistic RL (NeoRL), an approach based on the principle of optimism in the face of uncertainty. NeoRL uses well-calibrated probabilistic models and plans optimistically w.r.t. the epistemic uncertainty about the unknown dynamics. Under continuity and bounded energy assumptions on the system, we provide a first-of-its-kind regret bound of O(Gamma_T T) for general nonlinear systems with Gaussian process dynamics. We compare NeoRL to other baselines on several deep RL environments and empirically demonstrate that NeoRL achieves the optimal average cost while incurring the least regret.

Reward functions are difficult to design and often hard to align with human intent. Preference-based Reinforcement Learning (RL) algorithms address these problems by learning reward functions from human feedback. However, the majority of preference-based RL methods na\"ively combine supervised reward models with off-the-shelf RL algorithms. Contemporary approaches have sought to improve performance and query complexity by using larger and more complex reward architectures such as transformers. Instead of using highly complex architectures, we develop a new and parameter-efficient algorithm, Inverse Preference Learning (IPL), specifically designed for learning from offline preference data. Our key insight is that for a fixed policy, the Q-function encodes all information about the reward function, effectively making them interchangeable. Using this insight, we completely eliminate the need for a learned reward function. Our resulting algorithm is simpler and more parameter-efficient. Across a suite of continuous control and robotics benchmarks, IPL attains competitive performance compared to more complex approaches that leverage transformer-based and non-Markovian reward functions while having fewer algorithmic hyperparameters and learned network parameters. Our code is publicly released.

Meta-gradient Reinforcement Learning (RL) allows agents to self-tune their hyper-parameters in an online fashion during training. In this paper, we identify a bias in the meta-gradient of current meta-gradient RL approaches. This bias comes from using the critic that is trained using the meta-learned discount factor for the advantage estimation in the outer objective which requires a different discount factor. Because the meta-learned discount factor is typically lower than the one used in the outer objective, the resulting bias can cause the meta-gradient to favor myopic policies. We propose a simple solution to this issue: we eliminate this bias by using an alternative, outer value function in the estimation of the outer loss. To obtain this outer value function we add a second head to the critic network and train it alongside the classic critic, using the outer loss discount factor. On an illustrative toy problem, we show that the bias can cause catastrophic failure of current meta-gradient RL approaches, and show that our proposed solution fixes it. We then apply our method to a more complex environment and demonstrate that fixing the meta-gradient bias can significantly improve performance.

Large Language Models (LLMs) are now increasingly widely used to simulate personas in virtual environments, leveraging their instruction-following capability. However, we discovered that even state-of-the-art LLMs cannot simulate personas with reversed performance (e.g., student personas with low proficiency in educational settings), which impairs the simulation diversity and limits the practical applications of the simulated environments. In this work, using mathematical reasoning as a representative scenario, we propose the first benchmark dataset for evaluating LLMs on simulating personas with reversed performance, a capability that we dub "counterfactual instruction following". We evaluate both open-weight and closed-source LLMs on this task and find that LLMs, including the OpenAI o1 reasoning model, all struggle to follow counterfactual instructions for simulating reversedly performing personas. Intersectionally simulating both the performance level and the race population of a persona worsens the effect even further. These results highlight the challenges of counterfactual instruction following and the need for further research.

Deep Q-learning algorithms remain notoriously unstable, especially during early training when the maximization operator amplifies estimation errors. Inspired by bounded rationality theory and developmental learning, we introduce Sat-EnQ, a two-phase framework that first learns to be ``good enough'' before optimizing aggressively. In Phase 1, we train an ensemble of lightweight Q-networks under a satisficing objective that limits early value growth using a dynamic baseline, producing diverse, low-variance estimates while avoiding catastrophic overestimation. In Phase 2, the ensemble is distilled into a larger network and fine-tuned with standard Double DQN. We prove theoretically that satisficing induces bounded updates and cannot increase target variance, with a corollary quantifying conditions for substantial reduction. Empirically, Sat-EnQ achieves 3.8x variance reduction, eliminates catastrophic failures (0% vs 50% for DQN), maintains 79% performance under environmental noise}, and requires 2.5x less compute than bootstrapped ensembles. Our results highlight a principled path toward robust reinforcement learning by embracing satisficing before optimization.

Past analyses of reinforcement learning from human feedback (RLHF) assume that the human fully observes the environment. What happens when human feedback is based only on partial observations? We formally define two failure cases: deception and overjustification. Modeling the human as Boltzmann-rational w.r.t. a belief over trajectories, we prove conditions under which RLHF is guaranteed to result in policies that deceptively inflate their performance, overjustify their behavior to make an impression, or both. To help address these issues, we mathematically characterize how partial observability of the environment translates into (lack of) ambiguity in the learned return function. In some cases, accounting for partial observability makes it theoretically possible to recover the return function and thus the optimal policy, while in other cases, there is irreducible ambiguity. We caution against blindly applying RLHF in partially observable settings and propose research directions to help tackle these challenges.

Existing reinforcement learning (RL)-based post-training methods for large language models have advanced rapidly, yet their design has largely been guided by heuristics rather than systematic theoretical principles. This gap limits our understanding of the properties of the gradient estimators and the associated optimization algorithms, thereby constraining opportunities to improve training stability and overall performance. In this work, we provide a unified theoretical framework that characterizes the statistical properties of commonly used policy-gradient estimators under mild assumptions. Our analysis establishes unbiasedness, derives exact variance expressions, and yields an optimization-loss upper bound that enables principled reasoning about learning dynamics. Building on these results, we prove convergence guarantees and derive an adaptive learning-rate schedule governed by the signal-to-noise ratio (SNR) of gradients. We further show that the variance-optimal baseline is a gradient-weighted estimator, offering a new principle for variance reduction and naturally enhancing stability beyond existing methods. These insights motivate Optimal Baseline and Learning-Rate Policy Optimization (OBLR-PO), an algorithm that jointly adapts learning rates and baselines in a theoretically grounded manner. Experiments on Qwen3-4B-Base and Qwen3-8B-Base demonstrate consistent gains over existing policy optimization methods, validating that our theoretical contributions translate into practical improvements in large-scale post-training.