Daily Papers

The deployment of large language models (LLMs) in real-world applications is increasingly limited by their high inference cost. While recent advances in dynamic token-level computation allocation attempt to improve efficiency by selectively activating model components per token, existing methods rely on greedy routing--a myopic execute-or-skip mechanism that often leads to irreversible information loss and suboptimal token selection. This paper introduces informed routing, a new paradigm that proactively addresses these issues. The key insight is to assess not only a token's immediate importance but also its recoverability, i.e., how well its transformation can be approximated. To this end, we propose the Lightweight Feature Forecaster (LFF), a small predictive module that estimates a unit's output before routing decisions are made. This enables a flexible execute-or-approximate policy that preserves model fidelity while drastically reducing computation. Extensive experiments on both language modeling and reasoning tasks show that informed routing achieves state-of-the-art efficiency-performance trade-offs across multiple sparsity levels. Notably, even without final LoRA fine-tuning, our method matches or surpasses strong baselines that require full fine-tuning, all while reducing training time by over 50%. The code is available at: https://github.com/EIT-NLP/informed-routing

Retrieval-Augmented Generation (RAG) significantly improves the performance of Large Language Models (LLMs) on knowledge-intensive tasks. However, varying response quality across LLMs under RAG necessitates intelligent routing mechanisms, which select the most suitable model for each query from multiple retrieval-augmented LLMs via a dedicated router model. We observe that external documents dynamically affect LLMs' ability to answer queries, while existing routing methods, which rely on static parametric knowledge representations, exhibit suboptimal performance in RAG scenarios. To address this, we formally define the new retrieval-augmented LLM routing problem, incorporating the influence of retrieved documents into the routing framework. We propose RAGRouter, a RAG-aware routing design, which leverages document embeddings and RAG capability embeddings with contrastive learning to capture knowledge representation shifts and enable informed routing decisions. Extensive experiments on diverse knowledge-intensive tasks and retrieval settings show that RAGRouter outperforms the best individual LLM by 3.61% on average and existing routing methods by 3.29%-9.33%. With an extended score-threshold-based mechanism, it also achieves strong performance-efficiency trade-offs under low-latency constraints.

Inventory Routing Problem (IRP) is a crucial challenge in supply chain management as it involves optimizing efficient route selection while considering the uncertainty of inventory demand planning. To solve IRPs, usually a two-stage approach is employed, where demand is predicted using machine learning techniques first, and then an optimization algorithm is used to minimize routing costs. Our experiment shows machine learning models fall short of achieving perfect accuracy because inventory levels are influenced by the dynamic business environment, which, in turn, affects the optimization problem in the next stage, resulting in sub-optimal decisions. In this paper, we formulate and propose a decision-focused learning-based approach to solving real-world IRPs. This approach directly integrates inventory prediction and routing optimization within an end-to-end system potentially ensuring a robust supply chain strategy.

As a telecom provider, our company has a critical mission to maintain telecom services even during power outages. To accomplish the mission, it is essential to maintain the power of the telecom base stations. Here we consider a solution where electric vehicles (EVs) directly supply power to base stations by traveling to their locations. The goal is to find EV routes that minimize both the total travel distance of all EVs and the number of downed base stations. In this paper, we formulate this routing problem as a new variant of the Electric Vehicle Routing Problem (EVRP) and propose a solver that combines a rule-based vehicle selector and a reinforcement learning (RL)-based node selector. The rule of the vehicle selector ensures the exact environmental states when the selected EV starts to move. In addition, the node selection by the RL model enables fast route generation, which is critical in emergencies. We evaluate our solver on both synthetic datasets and real datasets. The results show that our solver outperforms baselines in terms of the objective value and computation time. Moreover, we analyze the generalization and scalability of our solver, demonstrating the capability toward unseen settings and large-scale problems. Check also our project page: https://ntt-dkiku.github.io/rl-evrpeps.

The rapid growth of large language models (LLMs) with diverse capabilities, costs, and domains has created a critical need for intelligent model selection at inference time. While smaller models suffice for routine queries, complex tasks demand more capable models. However, static model deployment does not account for the complexity and domain of incoming queries, leading to suboptimal performance and increased costs. Dynamic routing systems that adaptively select models based on query characteristics have emerged as a solution to this challenge. We provide a systematic analysis of state-of-the-art multi-LLM routing and cascading approaches. In contrast to mixture-of-experts architectures, which route within a single model, we study routing across multiple independently trained LLMs. We cover diverse routing paradigms, including query difficulty, human preferences, clustering, uncertainty quantification, reinforcement learning, multimodality, and cascading. For each paradigm, we analyze representative methods and examine key trade-offs. Beyond taxonomy, we introduce a conceptual framework that characterizes routing systems along three dimensions: when decisions are made, what information is used, and how they are computed. This perspective highlights that practical systems are often compositional, integrating multiple paradigms under operational constraints. Our analysis demonstrates that effective multi-LLM routing requires balancing competing objectives. Choosing the optimal routing strategy depends on deployment and computational constraints. Well-designed routing systems can outperform even the most powerful individual models by strategically leveraging specialized capabilities across models while maximizing efficiency gains. Meanwhile, open challenges remain in developing routing mechanisms that generalize across diverse architectures, modalities, and applications.

Recent advances in Large Reasoning Models (LRMs) have significantly improved long-chain reasoning capabilities over Large Language Models (LLMs). However, LRMs often produce unnecessarily lengthy outputs even for simple queries, leading to inefficiencies or even accuracy degradation compared to LLMs. To overcome this, we propose CP-Router, a training-free and model-agnostic routing framework that dynamically selects between an LLM and an LRM, demonstrated with multiple-choice question answering (MCQA) prompts. The routing decision is guided by the prediction uncertainty estimates derived via Conformal Prediction (CP), which provides rigorous coverage guarantees. To further refine the uncertainty differentiation across inputs, we introduce Full and Binary Entropy (FBE), a novel entropy-based criterion that adaptively selects the appropriate CP threshold. Experiments across diverse MCQA benchmarks, including mathematics, logical reasoning, and Chinese chemistry, demonstrate that CP-Router efficiently reduces token usage while maintaining or even improving accuracy compared to using LRM alone. We also extend CP-Router to diverse model pairings and open-ended QA, where it continues to demonstrate strong performance, validating its generality and robustness.

As large language models (LLMs) diversify across modalities, capabilities, and cost profiles, the problem of intelligent request routing -- selecting the right model for each query at inference time -- has become a critical systems challenge. We present vLLM Semantic Router, a signal-driven decision routing framework for Mixture-of-Modality (MoM) model deployments. The central innovation is composable signal orchestration: the system extracts heterogeneous signal types from each request -- from sub-millisecond heuristic features (keyword patterns, language detection, context length, role-based authorization) to neural classifiers (domain, embedding similarity, factual grounding, modality) -- and composes them through configurable Boolean decision rules into deployment-specific routing policies. Different deployment scenarios -- multi-cloud enterprise, privacy-regulated, cost-optimized, latency-sensitive -- are expressed as different signal-decision configurations over the same architecture, without code changes. Matched decisions drive semantic model routing: over a dozen of selection algorithms analyze request characteristics to find the best model cost-effectively, while per-decision plugin chains enforce privacy and safety constraints (jailbreak detection, PII filtering, hallucination detection via the three-stage HaluGate pipeline). The system provides OpenAI API support for stateful multi-turn conversations, multi-endpoint and multi-provider routing across heterogeneous backends (vLLM, OpenAI, Anthropic, Azure, Bedrock, Gemini, Vertex AI), and a pluggable authorization factory supporting multiple auth providers. Deployed in production as an Envoy external processor, the architecture demonstrates that composable signal orchestration enables a single routing framework to serve diverse deployment scenarios with differentiated cost, privacy, and safety policies.

With the rapid proliferation of large language models (LLMs) -- each optimized for different strengths, style, or latency/cost profile -- routing has become an essential technique to operationalize the use of different models. However, existing LLM routing approaches are limited in two key ways: they evaluate performance using benchmarks that often fail to capture human preferences driven by subjective evaluation criteria, and they typically select from a limited pool of models. In this work, we propose a preference-aligned routing framework that guides model selection by matching queries to user-defined domains (e.g., travel) or action types (e.g., image editing) -- offering a practical mechanism to encode preferences in routing decisions. Specifically, we introduce Arch-Router, a compact 1.5B model that learns to map queries to domain-action preferences for model routing decisions. Our approach also supports seamlessly adding new models for routing without requiring retraining or architectural modifications. Experiments on conversational datasets demonstrate that our approach achieves state-of-the-art (SOTA) results in matching queries with human preferences, outperforming top proprietary models. Our approach captures subjective evaluation criteria and makes routing decisions more transparent and flexible. Our model is available at: https://huggingface.co/katanemo/Arch-Router-1.5B.

Inverse reinforcement learning (IRL) offers a powerful and general framework for learning humans' latent preferences in route recommendation, yet no approach has successfully addressed planetary-scale problems with hundreds of millions of states and demonstration trajectories. In this paper, we introduce scaling techniques based on graph compression, spatial parallelization, and improved initialization conditions inspired by a connection to eigenvector algorithms. We revisit classic IRL methods in the routing context, and make the key observation that there exists a trade-off between the use of cheap, deterministic planners and expensive yet robust stochastic policies. This insight is leveraged in Receding Horizon Inverse Planning (RHIP), a new generalization of classic IRL algorithms that provides fine-grained control over performance trade-offs via its planning horizon. Our contributions culminate in a policy that achieves a 16-24% improvement in route quality at a global scale, and to the best of our knowledge, represents the largest published study of IRL algorithms in a real-world setting to date. We conclude by conducting an ablation study of key components, presenting negative results from alternative eigenvalue solvers, and identifying opportunities to further improve scalability via IRL-specific batching strategies.

Connected Autonomous Vehicles (CAVs) promise to reduce congestion in future urban networks, potentially by optimizing their routing decisions. Unlike for human drivers, these decisions can be made with collective, data-driven policies, developed by machine learning algorithms. Reinforcement learning (RL) can facilitate the development of such collective routing strategies, yet standardized and realistic benchmarks are missing. To that end, we present : Urban Routing Benchmark for RL-equipped Connected Autonomous Vehicles. is a comprehensive benchmarking environment that unifies evaluation across 29 real-world traffic networks paired with realistic demand patterns. comes with a catalog of predefined tasks, four state-of-the-art multi-agent RL (MARL) algorithm implementations, three baseline methods, domain-specific performance metrics, and a modular configuration scheme. Our results suggest that, despite the lengthy and costly training, state-of-the-art MARL algorithms rarely outperformed humans. Experimental results reported in this paper initiate the first leaderboard for MARL in large-scale urban routing optimization and reveal that current approaches struggle to scale, emphasizing the urgent need for advancements in this domain.

Over the past year, the vLLM Semantic Router project has released a series of work spanning: (1) core routing mechanisms -- signal-driven routing, context-length pool routing, router performance engineering, policy conflict detection, low-latency embedding models, category-aware semantic caching, user-feedback-driven routing adaptation, hallucination detection, and hierarchical content-safety classification for privacy and jailbreak protection; (2) fleet optimization -- fleet provisioning and energy-efficiency analysis; (3) agentic and multimodal routing -- multimodal agent routing, tool selection, CUA security, and multi-turn context memory and safety; (4) governance and standards -- inference routing protocols and multi-provider API extensions. Each paper tackled a specific problem in LLM inference, but the problems are not independent; for example, fleet provisioning depends on the routing policy, which depends on the workload mix, shifting as organizations adopt agentic and multimodal workloads. This paper distills those results into the Workload-Router-Pool (WRP) architecture, a three-dimensional framework for LLM inference optimization. Workload characterizes what the fleet serves (chat vs. agent, single-turn vs. multi-turn, warm vs. cold, prefill-heavy vs. decode-heavy). Router determines how each request is dispatched (static semantic rules, online bandit adaptation, RL-based model selection, quality-aware cascading). Pool defines where inference runs (homogeneous vs. heterogeneous GPU, disaggregated prefill/decode, KV-cache topology). We map our prior work onto a 3x3 WRP interaction matrix, identify which cells we have covered and which remain open, and propose twenty-one concrete research directions at the intersections, each grounded in our prior measurements, tiered by maturity from engineering-ready to open research.

Large language model (LLM) routers improve the efficiency of multi-model systems by directing each query to the most appropriate model while leveraging the diverse strengths of heterogeneous LLMs. Most existing approaches frame routing as a classification problem based solely on the input query. While this reduces overhead by avoiding inference across all models, it overlooks valuable information that could be gleaned from potential outputs and fails to capture implicit intent or contextual nuances that often emerge only during response generation. These limitations can result in suboptimal routing decisions, particularly for complex or ambiguous queries that require deeper semantic understanding. To address this challenge, we propose Lookahead, a routing framework that "foresees" potential model outputs by predicting their latent representations and uses these predictions to guide model selection, thus enabling more informed routing without full inference. Within this framework, we implement two approaches based on causal and masked language models. Empirical evaluations across seven public benchmarks - spanning instruction following, mathematical reasoning, and code generation - show that Lookahead consistently outperforms existing routing baselines, achieving an average performance gain of 7.7% over the state-of-the-art. Our code is available at https://github.com/huangcb01/lookahead-routing.

Modern LLM deployments confront a widening cost-performance spectrum: premium models deliver strong reasoning but are expensive, while lightweight models are economical yet brittle on complex tasks. Static escalation rules and keyword heuristics under-utilize this spectrum and fail to adapt across task types. We present xRouter, a tool-calling-based routing system in which a learned router can either answer directly or invoke one or more external models. The router is trained end-to-end with reinforcement learning using an explicit, cost-aware reward that encodes cost-performance trade-offs, eliminating the need for hand-engineered routing rules. Our implementation encompasses the full reinforcement learning framework, including reward and cost accounting, as well as the deployment and evaluation pipelines. Across diverse benchmarks, xRouter achieves strong cost-performance trade-offs (e.g., substantial cost reductions at comparable task completion rates), and provides empirical insights into what reliably helps learned routing and what does not, ranging from model trainability to the difficulty of eliciting sophisticated orchestration behaviors in small open models. We hope these findings and our open implementation will serve as a practical substrate for advancing learned, cost-aware LLM orchestration.

Robust routing under uncertainty is central to real-world logistics, yet most benchmarks assume static, idealized settings. We present SVRPBench, the first open benchmark to capture high-fidelity stochastic dynamics in vehicle routing at urban scale. Spanning more than 500 instances with up to 1000 customers, it simulates realistic delivery conditions: time-dependent congestion, log-normal delays, probabilistic accidents, and empirically grounded time windows for residential and commercial clients. Our pipeline generates diverse, constraint-rich scenarios, including multi-depot and multi-vehicle setups. Benchmarking reveals that state-of-the-art RL solvers like POMO and AM degrade by over 20% under distributional shift, while classical and metaheuristic methods remain robust. To enable reproducible research, we release the dataset and evaluation suite. SVRPBench challenges the community to design solvers that generalize beyond synthetic assumptions and adapt to real-world uncertainty.

Model routing chooses which language model to use for each query. By sending easy queries to cheaper models and hard queries to stronger ones, it can significantly reduce inference cost while maintaining high accuracy. However, most existing routers treat this as a fixed choice among a small set of models, which makes them hard to adapt to new models or changing budget constraints. In this paper, we propose SCOPE (Scalable and Controllable Outcome Performance Estimator), a routing framework that goes beyond model selection by predicting their cost and performance. Trained with reinforcement learning, SCOPE makes reasoning-based predictions by retrieving how models behave on similar problems, rather than relying on fixed model names, enabling it to work with new, unseen models. Moreover, by explicitly predicting how accurate and how expensive a model will be, it turns routing into a dynamic decision problem, allowing users to easily control the trade-off between accuracy and cost. Experiments show that SCOPE is more than just a cost-saving tool. It flexibly adapts to user needs: it can boost accuracy by up to 25.7% when performance is the priority, or cut costs by up to 95.1% when efficiency matters most.

Sparsely activated neural networks with conditional computation learn to route their inputs through different "expert" subnetworks, providing a form of modularity that densely activated models lack. Despite their possible benefits, models with learned routing often underperform their parameter-matched densely activated counterparts as well as models that use non-learned heuristic routing strategies. In this paper, we hypothesize that these shortcomings stem from the gradient estimation techniques used to train sparsely activated models that use non-differentiable discrete routing decisions. To address this issue, we introduce Soft Merging of Experts with Adaptive Routing (SMEAR), which avoids discrete routing by using a single "merged" expert constructed via a weighted average of all of the experts' parameters. By routing activations through a single merged expert, SMEAR does not incur a significant increase in computational costs and enables standard gradient-based training. We empirically validate that models using SMEAR outperform models that route based on metadata or learn sparse routing through gradient estimation. Furthermore, we provide qualitative analysis demonstrating that the experts learned via SMEAR exhibit a significant amount of specialization. All of the code used in our experiments is publicly available.

We formulate and solve the H-SARA Problem, a Vehicle Routing and Appointment Scheduling Problem motivated by home services management. We assume that travel times, service durations, and customer cancellations are stochastic. We use a two-stage process that first generates teams and routes using a VRP Solver with optional extensions and then uses an MC Scheduler that determines expected arrival times by teams at customers. We further introduce two different models of cancellation and their associated impacts on routing and scheduling. Finally, we introduce the Route Fracture Metaheuristic that iteratively improves an H-SARA solution by replacing the worst-performing teams. We present insights into the problem and a series of numerical experiments that illustrate properties of the optimal routing, scheduling, and the impact of the Route Fracture Metaheuristic for both models of cancellation.

The Vehicle Routing Problem (VRP) is a widely studied combinatorial optimization problem and has been applied to various practical problems. While the explainability for VRP is significant for improving the reliability and interactivity in practical VRP applications, it remains unexplored. In this paper, we propose RouteExplainer, a post-hoc explanation framework that explains the influence of each edge in a generated route. Our framework realizes this by rethinking a route as the sequence of actions and extending counterfactual explanations based on the action influence model to VRP. To enhance the explanation, we additionally propose an edge classifier that infers the intentions of each edge, a loss function to train the edge classifier, and explanation-text generation by Large Language Models (LLMs). We quantitatively evaluate our edge classifier on four different VRPs. The results demonstrate its rapid computation while maintaining reasonable accuracy, thereby highlighting its potential for deployment in practical applications. Moreover, on the subject of a tourist route, we qualitatively evaluate explanations generated by our framework. This evaluation not only validates our framework but also shows the synergy between explanation frameworks and LLMs. See https://ntt-dkiku.github.io/xai-vrp for our code, datasets, models, and demo.

This paper proposes a novel admission and routing scheme which takes into account arbitrarily assigned priorities for network flows. The presented approach leverages the centralized Software Defined Networking (SDN) capabilities in order to do so. Exact and heuristic approaches to the stated Priority Flow Admission and Routing (PFAR) problem are provided. The exact approach which provides an optimal solution is based on Integer Linear Programming (ILP). Given the potentially long running time required to find an exact and optimal solution, a heuristic approach is proposed; this approach is based on Genetic Algorithms (GAs). In order to effectively estimate the performance of the proposed approaches, a simulator that is capable of generating semi-random network topologies and flows has been developed. Experimental results for large problem instances (up 50 network nodes and thousands of network flows), show that: i) an optimal solution can be often found in few seconds (even milliseconds), and ii) the heuristic approach yields close-to-optimal solutions (approximately 95\% of the optimal) in a fixed amount of time; these experimental results demonstrate the pertinence of the proposed approaches.

Mixture of Experts models are widely assumed to achieve domain specialization through sparse routing. In this work, we question this assumption by introducing COMMITTEEAUDIT, a post hoc framework that analyzes routing behavior at the level of expert groups rather than individual experts. Across three representative models and the MMLU benchmark, we uncover a domain-invariant Standing Committee. This is a compact coalition of routed experts that consistently captures the majority of routing mass across domains, layers, and routing budgets, even when architectures already include shared experts. Qualitative analysis further shows that Standing Committees anchor reasoning structure and syntax, while peripheral experts handle domain-specific knowledge. These findings reveal a strong structural bias toward centralized computation, suggesting that specialization in Mixture of Experts models is far less pervasive than commonly believed. This inherent bias also indicates that current training objectives, such as load-balancing losses that enforce uniform expert utilization, may be working against the model's natural optimization path, thereby limiting training efficiency and performance.

Large Language Model (LLM)-driven Multi-Agent Systems (MAS) have demonstrated strong capability in complex reasoning and tool use, and heterogeneous agent pools further broaden the quality--cost trade-off space. Despite these advances, real-world deployment is often constrained by high inference cost, latency, and limited transparency, which hinders scalable and efficient routing. Existing routing strategies typically rely on expensive LLM-based selectors or static policies, and offer limited controllability for semantic-aware routing under dynamic loads and mixed intents, often resulting in unstable performance and inefficient resource utilization. To address these limitations, we propose AMRO-S, an efficient and interpretable routing framework for Multi-Agent Systems (MAS). AMRO-S models MAS routing as a semantic-conditioned path selection problem, enhancing routing performance through three key mechanisms: First, it leverages a supervised fine-tuned (SFT) small language model for intent inference, providing a low-overhead semantic interface for each query; second, it decomposes routing memory into task-specific pheromone specialists, reducing cross-task interference and optimizing path selection under mixed workloads; finally, it employs a quality-gated asynchronous update mechanism to decouple inference from learning, optimizing routing without increasing latency. Extensive experiments on five public benchmarks and high-concurrency stress tests demonstrate that AMRO-S consistently improves the quality--cost trade-off over strong routing baselines, while providing traceable routing evidence through structured pheromone patterns.

As LLMs proliferate with diverse capabilities and costs, LLM routing has emerged by learning to predict each LLM's quality and cost for a given query, then selecting the one with high quality and low cost. However, existing routers implicitly assume a single fixed quality and cost per LLM for each query, ignoring that the same LLM's quality varies with its output length. This causes routers to exclude powerful LLMs when their estimated cost exceeds the budget, missing the opportunity that these LLMs could still deliver high quality at reduced cost with shorter outputs. To address this, we introduce R2-Router, which treats output length budget as a controllable variable and jointly selects the best LLM and length budget, enforcing the budget via length-constrained instructions. This enables R2-Router to discover that a powerful LLM with constrained output can outperform a weaker LLM at comparable cost-efficient configurations invisible to prior methods. Together with the router framework, we construct R2-Bench, the first routing dataset capturing LLM behavior across diverse output length budgets. Experiments show that R2-Router achieves state-of-the-art performance at 4-5x lower cost compared with existing routers. This work opens a new direction: routing as reasoning, where routers evolve from reactive selectors to deliberate reasoners that explore which LLM to use and at what cost budget.

The proliferation of Large Language Models (LLMs) has established LLM routing as a standard service delivery mechanism, where users select models based on cost, Quality of Service (QoS), among other things. However, optimal pricing in LLM routing platforms requires precise modeling for dynamic service markets, and solving this problem in real time at scale is computationally intractable. In this paper, we propose \PriLLM, a novel practical and scalable solution for real-time dynamic pricing in competitive LLM routing. \PriLLM models the service market as a Stackelberg game, where providers set prices and users select services based on multiple criteria. To capture real-world market dynamics, we incorporate both objective factors (\eg~cost, QoS) and subjective user preferences into the model. For scalability, we employ a deep aggregation network to learn provider abstraction that preserve user-side equilibrium behavior across pricing strategies. Moreover, \PriLLM offers interpretability by explaining its pricing decisions. Empirical evaluation on real-world data shows that \PriLLM achieves over 95\% of the optimal profit while only requiring less than 5\% of the optimal solution's computation time.

The Vehicle Routing Problem (VRP) is one of the most intensively studied combinatorial optimisation problems for which numerous models and algorithms have been proposed. To tackle the complexities, uncertainties and dynamics involved in real-world VRP applications, Machine Learning (ML) methods have been used in combination with analytical approaches to enhance problem formulations and algorithmic performance across different problem solving scenarios. However, the relevant papers are scattered in several traditional research fields with very different, sometimes confusing, terminologies. This paper presents a first, comprehensive review of hybrid methods that combine analytical techniques with ML tools in addressing VRP problems. Specifically, we review the emerging research streams on ML-assisted VRP modelling and ML-assisted VRP optimisation. We conclude that ML can be beneficial in enhancing VRP modelling, and improving the performance of algorithms for both online and offline VRP optimisations. Finally, challenges and future opportunities of VRP research are discussed.

LLMs have shown impressive progress in robotics (e.g., manipulation and navigation) with natural language task descriptions. The success of LLMs in these tasks leads us to wonder: What is the ability of LLMs to solve vehicle routing problems (VRPs) with natural language task descriptions? In this work, we study this question in three steps. First, we construct a dataset with 21 types of single- or multi-vehicle routing problems. Second, we evaluate the performance of LLMs across four basic prompt paradigms of text-to-code generation, each involving different types of text input. We find that the basic prompt paradigm, which generates code directly from natural language task descriptions, performs the best for GPT-4, achieving 56% feasibility, 40% optimality, and 53% efficiency. Third, based on the observation that LLMs may not be able to provide correct solutions at the initial attempt, we propose a framework that enables LLMs to refine solutions through self-reflection, including self-debugging and self-verification. With GPT-4, our proposed framework achieves a 16% increase in feasibility, a 7% increase in optimality, and a 15% increase in efficiency. Moreover, we examine the sensitivity of GPT-4 to task descriptions, specifically focusing on how its performance changes when certain details are omitted from the task descriptions, yet the core meaning is preserved. Our findings reveal that such omissions lead to a notable decrease in performance: 4% in feasibility, 4% in optimality, and 5% in efficiency. Website: https://sites.google.com/view/words-to-routes/

Large Language Models (LLMs) have revolutionized natural language processing, but their varying capabilities and costs pose challenges in practical applications. LLM routing addresses this by dynamically selecting the most suitable LLM for each query/task. Previous approaches treat this as a supervised learning problem, assuming complete knowledge of optimal query-LLM pairings. However, real-world scenarios lack such comprehensive mappings and face evolving user queries. We thus propose to study LLM routing as a contextual bandit problem, enabling adaptive decision-making using bandit feedback without requiring exhaustive inference across all LLMs for all queries (in contrast to supervised routing). To address this problem, we develop a shared embedding space for queries and LLMs, where query and LLM embeddings are aligned to reflect their affinity. This space is initially learned from offline human preference data and refined through online bandit feedback. We instantiate this idea through Preference-prior Informed Linucb fOr adaptive rouTing (PILOT), a novel extension of LinUCB. To handle diverse user budgets for model routing, we introduce an online cost policy modeled as a multi-choice knapsack problem, ensuring resource-efficient routing.

This paper proposes a novel framework to predict traffic flows' bandwidth ahead of time. Modern network management systems share a common issue: the network situation evolves between the moment the decision is made and the moment when actions (countermeasures) are applied. This framework converts packets from real-life traffic into flows containing relevant features. Machine learning models, including Decision Tree, Random Forest, XGBoost, and Deep Neural Network, are trained on these data to predict the bandwidth at the next time instance for every flow. Predictions can be fed to the management system instead of current flows bandwidth in order to take decisions on a more accurate network state. Experiments were performed on 981,774 flows and 15 different time windows (from 0.03s to 4s). They show that the Random Forest is the best performing and most reliable model, with a predictive performance consistently better than relying on the current bandwidth (+19.73% in mean absolute error and +18.00% in root mean square error). Experimental results indicate that this framework can help network management systems to take more informed decisions using a predicted network state.

This study proposes a hybrid deep-learning-metaheuristic framework with a bi-level architecture for road network design problems (NDPs). We train a graph neural network (GNN) to approximate the solution of the user equilibrium (UE) traffic assignment problem and use inferences made by the trained model to calculate fitness function evaluations of a genetic algorithm (GA) to approximate solutions for NDPs. Using three test networks, two NDP variants and an exact solver as benchmark, we show that on average, our proposed framework can provide solutions within 1.5% gap of the best results in less than 0.5% of the time used by the exact solution procedure. Our framework can be utilized within an expert system for infrastructure planning to determine the best infrastructure planning and management decisions under different scenarios. Given the flexibility of the framework, it can easily be adapted to many other decision problems that can be modeled as bi-level problems on graphs. Moreover, we foreseen interesting future research directions, thus we also put forward a brief research agenda for this topic. The key observation from our research that can shape future research is that the fitness function evaluation time using the inferences made by the GNN model was in the order of milliseconds, which points to an opportunity and a need for novel heuristics that 1) can cope well with noisy fitness function values provided by deep learning models, and 2) can use the significantly enlarged efficiency of the evaluation step to explore the search space effectively (rather than efficiently). This opens a new avenue for a modern class of metaheuristics that are crafted for use with AI-powered predictors.

Multi-Agent Systems(MAS) have become a powerful paradigm for building high performance intelligent applications. Within these systems, the router responsible for determining which expert agents should handle a given query plays a crucial role in overall performance. Existing routing strategies generally fall into two categories: performance routing, which balances latency and cost across models of different sizes, and task routing, which assigns queries to domain-specific experts to improve accuracy. In real-world enterprise applications, task routing is more suitable; however, most existing approaches rely on static single-label decisions, which introduce two major limitations: (i) difficulty in seamlessly integrating new agents as business domains expand, and (ii) routing conflicts caused by overlapping agent capabilities, ultimately degrading accuracy and robustness.To address these challenges, we propose TCAndon-Router(TCAR): an adaptive reasoning router for multi-agent collaboration. Unlike traditional routers, TCAR supports dynamic agent onboarding and first generates a natural-language reasoning chain before predicting a set of candidate agents capable of handling the query. In addition, we design a collaborative execution pipeline in which selected agents independently produce responses, which are then aggregated and refined into a single high-quality response by a dedicated Refining Agent.Experiments on public datasets and real enterprise data demonstrate that TCAR significantly improves routing accuracy, reduces routing conflicts, and remains robust in ambiguous scenarios. We have released TCAR at https://huggingface.co/tencent/TCAndon-Router to support future research on explainable and collaborative multi-agent routing.

Mixture-of-Experts layers achieve compute efficiency through weight sparsity: each token activates only a subset of experts. Data sparsity, where each expert processes only a subset of tokens, offers a complementary axis. Expert-choice routing implements data sparsity directly but violates causality in autoregressive models, creating train-inference mismatch. We recover data sparsity within causal token-choice MoE by leveraging zero-compute (null) experts within the routing pool. When a token routes to null experts, those slots consume no compute. The standard load balancing objective trains the model to uniformly use all experts (real and null) therefore creating data sparsity in expectation without the causality violations. We evaluate on vision-language model training, where data heterogeneity is pronounced: vision encoders produce many low-information tokens while text tokens are denser. At matched expected FLOPs, composing weight and data sparsity yields a more compute-efficient frontier than weight sparsity alone, with gains in training loss and downstream performance. The model learns implicit modality-aware allocation, routing vision tokens to null experts more aggressively than text, without explicit modality routing.

Motivated by the operational problems in click and collect systems, such as curbside pickup programs, we study a joint admission control and capacity allocation problem. We consider a system where arriving customers have preferred service delivery times and gauge the service quality based on the service provider's ability to complete the service as close as possible to the preferred time. Customers can be of different priority classes, and their priority may increase as they wait longer in the queue. The service provider can reject customers upon their arrival if the system is overloaded or outsource the service (alternatively work overtime) when the capacity is not enough. The service provider's goal is to find the minimum-cost admission and capacity allocation policy to dynamically decide when to serve and whom to serve. We model this problem as a Markov Decision Process. Our structural results partially characterize a set of suboptimal solutions, and we develop solution methods using these results. We also develop a problem-specific approximation method that is based on state aggregation to overcome the computational challenges. We present extensive computational results and discuss the impact of problem parameters on the optimal policy.

Large language models' significant advances in capabilities are accompanied by significant increases in inference costs. Model routing is a simple technique for reducing inference cost, wherein one maintains a pool of candidate LLMs, and learns to route each prompt to the smallest feasible LLM. Existing works focus on learning a router for a fixed pool of LLMs. In this paper, we consider the problem of dynamic routing, where new, previously unobserved LLMs are available at test time. We propose a new approach to this problem that relies on representing each LLM as a feature vector, derived based on predictions on a set of representative prompts. Based on this, we detail two effective strategies, relying on cluster-based routing and a learned cluster map respectively. We prove that these strategies are estimates of a theoretically optimal routing rule, and provide an excess risk bound to quantify their errors. Experiments on a range of public benchmarks show the effectiveness of the proposed strategies in routing amongst more than 30 unseen LLMs.

With the rapid growth in the number of Large Language Models (LLMs), there has been a recent interest in LLM routing, or directing queries to the cheapest LLM that can deliver a suitable response. Following this line of work, we introduce CARROT, a Cost AwaRe Rate Optimal rouTer that can select models based on any desired trade-off between performance and cost. Given a query, CARROT selects a model based on estimates of models' cost and performance. Its simplicity lends CARROT computational efficiency, while our theoretical analysis demonstrates minimax rate-optimality in its routing performance. Alongside CARROT, we also introduce the Smart Price-aware Routing (SPROUT) dataset to facilitate routing on a wide spectrum of queries with the latest state-of-the-art LLMs. Using SPROUT and prior benchmarks such as Routerbench and open-LLM-leaderboard-v2 we empirically validate CARROT's performance against several alternative routers.

The rapid advancement in large language models (LLMs) has brought forth a diverse range of models with varying capabilities that excel in different tasks and domains. However, selecting the optimal LLM for user queries often involves a challenging trade-off between accuracy and cost, a problem exacerbated by the diverse demands of individual queries. In this work, we present a novel framework that formulates the LLM selection process as a multi-armed bandit problem, enabling dynamic and intelligent routing of queries to the most appropriate model. Our approach incorporates a preference-conditioned dynamic routing mechanism, allowing users to specify their preferences at inference time, thereby offering a customizable balance between performance and cost. Additionally, our selection policy is designed to generalize to unseen LLMs, ensuring adaptability to new models as they emerge. Experimental results demonstrate that our method achieves significant improvements in both accuracy and cost-effectiveness across various LLM platforms, showcasing the potential of our framework to adaptively optimize LLM selection in real-world scenarios.

Recent advancements in Large Language Models (LLMs) have demonstrated their potential in planning and reasoning tasks, offering a flexible alternative to classical pathfinding algorithms. However, most existing studies focus on LLMs' independent reasoning capabilities and overlook the potential synergy between LLMs and traditional algorithms. To fill this gap, we propose a comprehensive evaluation benchmark GridRoute to assess how LLMs can take advantage of traditional algorithms. We also propose a novel hybrid prompting technique called Algorithm of Thought (AoT), which introduces traditional algorithms' guidance into prompting. Our benchmark evaluates six LLMs ranging from 7B to 72B parameters across various map sizes, assessing their performance in correctness, optimality, and efficiency in grid environments with varying sizes. Our results show that AoT significantly boosts performance across all model sizes, particularly in larger or more complex environments, suggesting a promising approach to addressing path planning challenges. Our code is open-sourced at https://github.com/LinChance/GridRoute.

Network systems form the foundation of modern society, playing a critical role in various applications. However, these systems are at significant risk of being adversely affected by unforeseen circumstances, such as disasters. Considering this, there is a pressing need for research to enhance the robustness of network systems. Recently, in reinforcement learning, the relationship between acquiring robustness and regularizing entropy has been identified. Additionally, imitation learning is used within this framework to reflect experts' behavior. However, there are no comprehensive studies on the use of a similar imitation framework for optimal transport on networks. Therefore, in this study, imitation-regularized optimal transport (I-OT) on networks was investigated. It encodes prior knowledge on the network by imitating a given prior distribution. The I-OT solution demonstrated robustness in terms of the cost defined on the network. Moreover, we applied the I-OT to a logistics planning problem using real data. We also examined the imitation and apriori risk information scenarios to demonstrate the usefulness and implications of the proposed method.

The availability of performant pre-trained models has led to a proliferation of fine-tuned expert models that are specialized to particular domains. This has enabled the creation of powerful and adaptive routing-based "Model MoErging" methods with the goal of using expert modules to create an aggregate system with improved performance or generalization. However, existing MoErging methods often prioritize generalization to unseen tasks at the expense of performance on held-in tasks, which limits its practical applicability in real-world deployment scenarios. We observe that current token-level routing mechanisms neglect the global semantic context of the input task. This token-wise independence hinders effective expert selection for held-in tasks, as routing decisions fail to incorporate the semantic properties of the task. To address this, we propose, Global and Local Instruction Driven Expert Router (GLIDER) that integrates a multi-scale routing mechanism, encompassing a semantic global router and a learned local router. The global router leverages LLM's advanced reasoning capabilities for semantic-related contexts to enhance expert selection. Given the input query and LLM, the router generates semantic task instructions that guide the retrieval of the most relevant experts across all layers. This global guidance is complemented by a local router that facilitates token-level routing decisions within each module, enabling finer control and enhanced performance on unseen tasks. Our experiments using T5-based models for T0 and FLAN tasks demonstrate that GLIDER achieves substantially improved held-in performance while maintaining strong generalization on held-out tasks. We also perform ablations experiments to dive deeper into the components of GLIDER. Our experiments highlight the importance of our multi-scale routing that leverages LLM-driven semantic reasoning for MoErging methods.

Cost-aware routing dynamically dispatches user queries to models of varying capability to balance performance and inference cost. However, the routing strategy introduces a new security concern that adversaries may manipulate the router to consistently select expensive high-capability models. Existing routing attacks depend on either white-box access or heuristic prompts, rendering them ineffective in real-world black-box scenarios. In this work, we propose R^2A, which aims to mislead black-box LLM routers to expensive models via adversarial suffix optimization. Specifically, R^2A deploys a hybrid ensemble surrogate router to mimic the black-box router. A suffix optimization algorithm is further adapted for the ensemble-based surrogate. Extensive experiments on multiple open-source and commercial routing systems demonstrate that {R^2A} significantly increases the routing rate to expensive models on queries of different distributions. Code and examples: https://github.com/thcxiker/R2A-Attack.

In modern logistics management systems, route planning requires high efficiency. The Open Capacitated Vehicle Routing Problem (OCVRP) deals with finding optimal delivery routes for a fleet of vehicles serving geographically distributed customers, without requiring the vehicles to return to the depot after deliveries. The present study is comparative in nature and speaks of two algorithms for OCVRP solution: Ant Colony Optimization (ACO), a nature-inspired metaheuristic; and Google OR-Tools, an industry-standard toolkit for optimization. Both implementations were developed in Python and using a custom dataset. Performance appraisal was based on routing efficiency, computation time, and scalability. The results show that ACO allows flexibility in routing parameters while OR-Tools runs much faster with more consistency and requires less input. This could help choose among routing strategies for scalable real-time logistics systems.

Fleets of robo-taxis offering on-demand transportation services, commonly known as Autonomous Mobility-on-Demand (AMoD) systems, hold significant promise for societal benefits, such as reducing pollution, energy consumption, and urban congestion. However, orchestrating these systems at scale remains a critical challenge, with existing coordination algorithms often failing to exploit the systems' full potential. This work introduces a novel decision-making framework that unites mathematical modeling with data-driven techniques. In particular, we present the AMoD coordination problem through the lens of reinforcement learning and propose a graph network-based framework that exploits the main strengths of graph representation learning, reinforcement learning, and classical operations research tools. Extensive evaluations across diverse simulation fidelities and scenarios demonstrate the flexibility of our approach, achieving superior system performance, computational efficiency, and generalizability compared to prior methods. Finally, motivated by the need to democratize research efforts in this area, we release publicly available benchmarks, datasets, and simulators for network-level coordination alongside an open-source codebase designed to provide accessible simulation platforms and establish a standardized validation process for comparing methodologies. Code available at: https://github.com/StanfordASL/RL4AMOD

Efficient use of large language models (LLMs) is critical for deployment at scale: without adaptive routing, systems either overpay for strong models or risk poor performance from weaker ones. Selecting the right LLM for each query is fundamentally an online decision problem: models differ in strengths, prices fluctuate, and users value accuracy and cost differently. Yet most routers are trained offline with labels for all candidate models, an assumption that breaks in deployment, where only the outcome of the chosen model is observed. We bridge this gap with BaRP, a Bandit-feedback Routing with Preferences approach that trains under the same partial-feedback restriction as deployment, while supporting preference-tunable inference: operators can dial the performance/cost trade-off at test time without retraining. Framed as a contextual bandit over prompt features and a user preference vector, our method simulates an online feedback setting during training and adapts its routing decisions to each new prompt, rather than depending on full-information offline supervision. Comprehensive experiments show that our method consistently outperforms strong offline routers by at least 12.46% and the largest LLM by at least 2.45%, and generalizes robustly for unseen tasks.

We study the problem of designing mechanisms for information acquisition scenarios. This setting models strategic interactions between an uniformed receiver and a set of informed senders. In our model the senders receive information about the underlying state of nature and communicate their observation (either truthfully or not) to the receiver, which, based on this information, selects an action. Our goal is to design mechanisms maximizing the receiver's utility while incentivizing the senders to report truthfully their information. First, we provide an algorithm that efficiently computes an optimal incentive compatible (IC) mechanism. Then, we focus on the online problem in which the receiver sequentially interacts in an unknown game, with the objective of minimizing the cumulative regret w.r.t. the optimal IC mechanism, and the cumulative violation of the incentive compatibility constraints. We investigate two different online scenarios, i.e., the full and bandit feedback settings. For the full feedback problem, we propose an algorithm that guarantees mathcal O(sqrt T) regret and violation, while for the bandit feedback setting we present an algorithm that attains mathcal O(T^{alpha}) regret and mathcal O(T^{1-alpha/2}) violation for any alphain[1/2, 1]. Finally, we complement our results providing a tight lower bound.

Data-driven optimization uses contextual information and machine learning algorithms to find solutions to decision problems with uncertain parameters. While a vast body of work is dedicated to interpreting machine learning models in the classification setting, explaining decision pipelines involving learning algorithms remains unaddressed. This lack of interpretability can block the adoption of data-driven solutions as practitioners may not understand or trust the recommended decisions. We bridge this gap by introducing a counterfactual explanation methodology tailored to explain solutions to data-driven problems. We introduce two classes of explanations and develop methods to find nearest explanations of random forest and nearest-neighbor predictors. We demonstrate our approach by explaining key problems in operations management such as inventory management and routing.

We study LLM routing, the problem of selecting the best model for each query while balancing user satisfaction, model expertise, and inference cost. We formulate routing as contextual dueling bandits, learning from pairwise preference feedback rather than absolute scores, thereby yielding label-efficient and dynamic adaptation. Building on this formulation, we introduce Category-Calibrated Fine-Tuning (CCFT), a representation-learning method that derives model embeddings from offline data using contrastive fine-tuning with categorical weighting. These embeddings enable the practical instantiation of Feel-Good Thompson Sampling for Contextual Dueling Bandits (FGTS.CDB), a theoretically grounded posterior-sampling algorithm. We propose four variants of the categorical weighting that explicitly integrate model quality and cost, and we empirically evaluate the proposed methods on the RouterBench and MixInstruct datasets. Across both benchmarks, our methods achieve lower cumulative regret and faster convergence, with better robustness and performance-cost balance than strong baselines built with a general-purpose OpenAI embedding model.

Recent advances in large-scale language models (LLMs) have made multi-agent architectures attractive for challenging reasoning tasks. However, many existing systems rely on stochastic routing or ad-hoc heuristics, making their behavior difficult to reproduce and their decision process hard to interpret. We propose ORCH, a deterministic coordination framework for discrete-choice reasoning that orchestrates heterogeneous LLMs. ORCH follows a ``many analyses, one decision'' paradigm: multiple base models independently produce structured analyses, and a dedicated merge agent outputs the final choice. The framework uses fixed rules for task decomposition and answer aggregation, keeping the pipeline predictable, reproducible, and training-free. Determinism here refers to fixed routing and aggregation rules under a fixed evaluation protocol, rather than strict bit-level reproducibility across deployments. To exploit model complementarity, we optionally introduce an EMA-guided router that updates agent selection using historical accuracy, latency, or cost; since it relies on answer-based feedback, it is mainly intended for benchmarking, controlled evaluation, or delayed-feedback settings. Experiments on MMLU, MMLU-Pro, and GSM8K show that ORCH consistently outperforms single-model baselines and a majority-vote ensemble. On MMLU-Pro, ORCH improves accuracy by over 10 points compared to the strongest baseline, and on GSM8K it yields gains exceeding 50 points; McNemar tests confirm statistical significance. The EMA router provides an additional 0.7--2.0 point accuracy boost, and ablations show that both multi-agent collaboration and routing contribute substantially. Overall, ORCH offers a practical path toward controllable, interpretable, and deployment-ready LLM-based agent systems for discrete-choice reasoning.

As large language models (LLMs) evolve into autonomous agents that execute long-horizon workflows, invoking a high-capability model at every step becomes economically unsustainable. While model routing is effective for single-turn queries, agentic routing is a sequential, path-dependent problem: early mistakes compound, feedback is often at the end of the episode, and deployments often demand strict per-task spending limits. We propose Budget-Aware Agentic Routing, which selects between a cheap and an expensive model at each step to optimize the cost--success frontier and to operate under strict per-task budgets. We propose Boundary-Guided Training, which leverages two boundary policies (always-small vs.\ always-large) to build a difficulty taxonomy and to anchor learning under sparse rewards. Our approach warms start with boundary-guided SFT data synthesis via stratified sampling of cost-efficient trajectories, then applies Boundary-Guided Policy Optimization (BoPO), combining boundary-relative rewards with a reference-guided advantage to avoid degenerate cheap-failure solutions. Experiment results show that our method improves the efficiency frontier, matching strong routing baselines at substantially lower cost while demonstrating generalization to strict inference-time budget constraints. Overall, our work establishes a foundational framework for agentic routing, shifting the paradigm from static model selection to dynamic, budget-aware sequential decision-making.

Large Language Models (LLM)-based systems, i.e. interconnected elements that include an LLM as a central component (e.g., conversational agents), are typically monolithic static architectures that rely on a single LLM for all user queries. However, they often require different preprocessing strategies, levels of reasoning, or knowledge. Generalist LLMs (i.e. GPT-4), trained on very large multi-topic corpora, can perform well in a variety of tasks. However, they require significant financial, energy, and hardware resources that may not be justified for basic tasks. This implies potentially investing in unnecessary costs for a given query. To overcome this problem, a routing mechanism routes user queries to the most suitable components, such as smaller LLMs or experts in specific topics. This approach may improve response quality while minimising costs. Routing can be expanded to other components of the conversational agent architecture, such as the selection of optimal embedding strategies. This paper explores key considerations for integrating routing into LLM-based systems, focusing on resource management, cost definition, and strategy selection. Our main contributions include a formalisation of the problem, a novel taxonomy of existing approaches emphasising relevance and resource efficiency, and a comparative analysis of these strategies in relation to industry practices. Finally, we identify critical challenges and directions for future research.

Travel planning is a sophisticated decision-making process that requires synthesizing multifaceted information to construct itineraries. However, existing travel planning approaches face several challenges: (1) Pruning candidate points of interest (POIs) while maintaining a high recall rate; (2) A single reasoning path restricts the exploration capability within the feasible solution space for travel planning; (3) Simultaneously optimizing hard constraints and soft constraints remains a significant difficulty. To address these challenges, we propose TourPlanner, a comprehensive framework featuring multi-path reasoning and constraint-gated reinforcement learning. Specifically, we first introduce a Personalized Recall and Spatial Optimization (PReSO) workflow to construct spatially-aware candidate POIs' set. Subsequently, we propose Competitive consensus Chain-of-Thought (CCoT), a multi-path reasoning paradigm that improves the ability of exploring the feasible solution space. To further refine the plan, we integrate a sigmoid-based gating mechanism into the reinforcement learning stage, which dynamically prioritizes soft-constraint satisfaction only after hard constraints are met. Experimental results on travel planning benchmarks demonstrate that TourPlanner achieves state-of-the-art performance, significantly surpassing existing methods in both feasibility and user-preference alignment.

Large language model (LLM) routing has emerged as a crucial strategy for balancing computational costs with performance by dynamically assigning queries to the most appropriate model based on query complexity. Despite recent advances showing that preference-data-based routers can outperform traditional methods, current evaluation benchmarks remain limited. They largely focus on general model capabilities while overlooking task-specific behaviors and critical concerns such as privacy, safety, and potential backdoor vulnerabilities introduced through preference data. In response, we propose the DSC benchmark: Diverse, Simple, and Categorized, an evaluation framework that categorizes router performance across a broad spectrum of query types, including coding, translation, mathematics, human instructions, general knowledge, and LLM jailbreaking. Additionally, it integrates privacy and safety assessments to reveal hidden risks. Our experiments on three preference-based routers and two commercial counterparts demonstrate that while these systems improve efficiency, they often make suboptimal, category-driven decisions. For instance, a BERT-based router directs all coding and mathematics queries to the most powerful LLM even when simpler models would suffice, while routing jailbreaking attempts to weaker models, thereby elevating safety risks.

We give a deterministic O(mlog^{2/3}n)-time algorithm for single-source shortest paths (SSSP) on directed graphs with real non-negative edge weights in the comparison-addition model. This is the first result to break the O(m+nlog n) time bound of Dijkstra's algorithm on sparse graphs, showing that Dijkstra's algorithm is not optimal for SSSP.

This paper develops a graph reinforcement learning approach to online planning of the schedule and destinations of electric aircraft that comprise an urban air mobility (UAM) fleet operating across multiple vertiports. This fleet scheduling problem is formulated to consider time-varying demand, constraints related to vertiport capacity, aircraft capacity and airspace safety guidelines, uncertainties related to take-off delay, weather-induced route closures, and unanticipated aircraft downtime. Collectively, such a formulation presents greater complexity, and potentially increased realism, than in existing UAM fleet planning implementations. To address these complexities, a new policy architecture is constructed, primary components of which include: graph capsule conv-nets for encoding vertiport and aircraft-fleet states both abstracted as graphs; transformer layers encoding time series information on demand and passenger fare; and a Multi-head Attention-based decoder that uses the encoded information to compute the probability of selecting each available destination for an aircraft. Trained with Proximal Policy Optimization, this policy architecture shows significantly better performance in terms of daily averaged profits on unseen test scenarios involving 8 vertiports and 40 aircraft, when compared to a random baseline and genetic algorithm-derived optimal solutions, while being nearly 1000 times faster in execution than the latter.

Vehicle Routing Problems (VRPs) are a class of NP-hard problems ubiquitous in several real-world logistics scenarios that pose significant challenges for optimization. Neural Combinatorial Optimization (NCO) has emerged as a promising alternative to classical approaches, as it can learn fast heuristics to solve VRPs. However, most research works in NCO for VRPs focus on simplified settings, which do not account for asymmetric distances and travel durations that cannot be derived by simple Euclidean distances and unrealistic data distributions, hindering real-world deployment. This work introduces RRNCO (Real Routing NCO) to bridge the gap of NCO between synthetic and real-world VRPs in the critical aspects of both data and modeling. First, we introduce a new, openly available dataset with real-world data containing a diverse dataset of locations, distances, and duration matrices from 100 cities, considering realistic settings with actual routing distances and durations obtained from Open Source Routing Machine (OSRM). Second, we propose a novel approach that efficiently processes both node and edge features through contextual gating, enabling the construction of more informed node embedding, and we finally incorporate an Adaptation Attention Free Module (AAFM) with neural adaptive bias mechanisms that effectively integrates not only distance matrices but also angular relationships between nodes, allowing our model to capture rich structural information. RRNCO achieves state-of-the-art results in real-world VRPs among NCO methods. We make our dataset and code publicly available at https://github.com/ai4co/real-routing-nco.

Motivated by concerns about making online decisions that incur undue amount of risk at each time step, in this paper, we formulate the probably anytime-safe stochastic combinatorial semi-bandits problem. In this problem, the agent is given the option to select a subset of size at most K from a set of L ground items. Each item is associated to a certain mean reward as well as a variance that represents its risk. To mitigate the risk that the agent incurs, we require that with probability at least 1-delta, over the entire horizon of time T, each of the choices that the agent makes should contain items whose sum of variances does not exceed a certain variance budget. We call this probably anytime-safe constraint. Under this constraint, we design and analyze an algorithm {\sc PASCombUCB} that minimizes the regret over the horizon of time T. By developing accompanying information-theoretic lower bounds, we show that under both the problem-dependent and problem-independent paradigms, {\sc PASCombUCB} is almost asymptotically optimal. Experiments are conducted to corroborate our theoretical findings. Our problem setup, the proposed {\sc PASCombUCB} algorithm, and novel analyses are applicable to domains such as recommendation systems and transportation in which an agent is allowed to choose multiple items at a single time step and wishes to control the risk over the whole time horizon.

In this paper, we present a new technique to obtain upper bounds on undirected unicast network information capacity. Using this technique, we characterize an upper bound, called partition bound, on the symmetric rate of information flow in undirected unicast networks and give an algorithm to compute it. Two classes of networks are presented for which the bound is tight and the capacity is achievable by routing thus confirming the undirected unicast conjecture for these classes of networks. We also show that the bound can be loose in general and present an approach to tighten it.

Vehicle Routing Problems (VRP) are an extension of the Traveling Salesperson Problem and are a fundamental NP-hard challenge in combinatorial optimization. Solving VRP in real-time at large scale has become critical in numerous applications, from growing markets like last-mile delivery to emerging use-cases like interactive logistics planning. Such applications involve solving similar problem instances repeatedly, yet current state-of-the-art solvers treat each instance on its own without leveraging previous examples. We introduce a novel optimization framework that uses a reinforcement learning agent - trained on prior instances - to quickly generate initial solutions, which are then further optimized by genetic algorithms. Our framework, Evolutionary Algorithm with Reinforcement Learning Initialization (EARLI), consistently outperforms current state-of-the-art solvers across various time scales. For example, EARLI handles vehicle routing with 500 locations within 1s, 10x faster than current solvers for the same solution quality, enabling applications like real-time and interactive routing. EARLI can generalize to new data, as demonstrated on real e-commerce delivery data of a previously unseen city. Our hybrid framework presents a new way to combine reinforcement learning and genetic algorithms, paving the road for closer interdisciplinary collaboration between AI and optimization communities towards real-time optimization in diverse domains.

Recent work explores latent reasoning to improve reasoning efficiency by replacing explicit reasoning trajectories with continuous representations in a latent space, yet its effectiveness varies across settings. Analysis of model confidence dynamics under latent reasoning reveals that thinking trajectories ending in incorrect answers contain fewer low-confidence steps than those ending in correct answers. Meanwhile, we suggest that soft embeddings aggregated by multiple low-confidence thinking alternatives may introduce and propagate noise, leading to high confidence in unreliable reasoning trajectories. Motivated by these observations, ThinkRouter, an inference-time confidence-aware routing mechanism is proposed to avoid high confidence and noise for efficient reasoning. ThinkRouter routes thinking to the discrete token space when model confidence is low, and to the latent space otherwise. Extensive experiments on STEM reasoning and coding benchmarks across diverse large reasoning models demonstrate that ThinkRouter outperforms explicit CoT, random routing, and latent reasoning baselines in terms of accuracy, achieving an average improvement of 19.70 points in Pass@1, while reducing generation length by up to 15.55%. Further comprehensive analysis reveals that ThinkRouter can calibrate errors arising from explicit CoT and latent reasoning, and accelerates end-of-thinking token generation by globally lowering model confidence.

Rapidly-exploring random trees (RRTs) are popular in motion planning because they find solutions efficiently to single-query problems. Optimal RRTs (RRT*s) extend RRTs to the problem of finding the optimal solution, but in doing so asymptotically find the optimal path from the initial state to every state in the planning domain. This behaviour is not only inefficient but also inconsistent with their single-query nature. For problems seeking to minimize path length, the subset of states that can improve a solution can be described by a prolate hyperspheroid. We show that unless this subset is sampled directly, the probability of improving a solution becomes arbitrarily small in large worlds or high state dimensions. In this paper, we present an exact method to focus the search by directly sampling this subset. The advantages of the presented sampling technique are demonstrated with a new algorithm, Informed RRT*. This method retains the same probabilistic guarantees on completeness and optimality as RRT* while improving the convergence rate and final solution quality. We present the algorithm as a simple modification to RRT* that could be further extended by more advanced path-planning algorithms. We show experimentally that it outperforms RRT* in rate of convergence, final solution cost, and ability to find difficult passages while demonstrating less dependence on the state dimension and range of the planning problem.

The rapid emergence of diverse large language models (LLMs) has spurred the development of LLM routers that assign user queries to the most suitable model. However, existing LLM routers typically perform a single-round, one-to-one mapping (i.e., assigning each query to a single model in isolation), which limits their capability to tackle complex tasks that demand the complementary strengths of multiple LLMs. In this paper, we present Router-R1, a reinforcement learning (RL)-based framework that formulates multi-LLM routing and aggregation as a sequential decision process. Router-R1 instantiates the router itself as a capable LLM, leveraging its reasoning ability to interleave "think" actions (internal deliberation) with "route" actions (dynamic model invocation), and integrates each response into its evolving context. To guide learning, we employ a lightweight rule-based reward comprising format rewards, final outcome rewards, and a novel cost reward for performance and cost trade-off optimization, opening a pathway toward optimizing performance-cost tradeoffs via RL. Router-R1 also conditions only on simple model descriptors such as pricing, latency, and example performance, enabling strong generalization to unseen model selection. Experiments on seven general and multi-hop QA benchmarks show that Router-R1 outperforms over several strong baselines, achieving superior performance while maintaining robust generalization and cost management.Code is available at https://github.com/ulab-uiuc/Router-R1.

Compound AI systems promise capabilities beyond those of individual models, yet their success depends critically on effective orchestration. Existing routing approaches face two limitations: (1) input-level routers make coarse query-level decisions that ignore evolving task requirements; (2) RL-trained orchestrators are expensive to adapt and often suffer from routing collapse, repeatedly invoking one strong but costly option in multi-turn scenarios. We introduce SkillOrchestra, a framework for skill-aware orchestration. Instead of directly learning a routing policy end-to-end, SkillOrchestra learns fine-grained skills from execution experience and models agent-specific competence and cost under those skills. At deployment, the orchestrator infers the skill demands of the current interaction and selects agents that best satisfy them under an explicit performance-cost trade-off. Extensive experiments across ten benchmarks demonstrate that SkillOrchestra outperforms SoTA RL-based orchestrators by up to 22.5% with 700x and 300x learning cost reduction compared to Router-R1 and ToolOrchestra, respectively. These results show that explicit skill modeling enables scalable, interpretable, and sample-efficient orchestration, offering a principled alternative to data-intensive RL-based approaches. The code is available at: https://github.com/jiayuww/SkillOrchestra.

Reasoning language models have demonstrated remarkable performance on many challenging tasks in math, science, and coding. Choosing the right reasoning model for practical deployment involves a performance and cost tradeoff at two key levels: model size and reasoning budget, where larger models and higher reasoning budget lead to better performance but with increased cost and latency. In this work, we tackle this tradeoff from the angle of model configuration routing for different queries, and present RADAR (Reasoning-Ability and Difficulty-Aware Routing), a lightweight, interpretable, and scalable routing framework. Inspired by psychometrics, RADAR learns an item response model from model responses with different budgets to different queries, with interpretable parameters including query difficulties and model-budget abilities. RADAR then routes queries with higher difficulty to model-budget pairs with higher ability, and vice versa. We conduct extensive experiments on 8 widely used challenging reasoning benchmarks, demonstrating the superior performance of RADAR compared to state-of-the-art model routing methods. RADAR also exhibits query generalization capabilities, showing strong performance on out-of-distribution queries in all benchmarks. RADAR is also scalable and can efficiently integrate additional models by dynamically selecting a small set of evaluation queries to estimate their abilities.

Reinforcement learning has been applied in operation research and has shown promise in solving large combinatorial optimization problems. However, existing works focus on developing neural network architectures for certain problems. These works lack the flexibility to incorporate recent advances in reinforcement learning, as well as the flexibility of customizing model architectures for operation research problems. In this work, we analyze the end-to-end autoregressive models for vehicle routing problems and show that these models can benefit from the recent advances in reinforcement learning with a careful re-implementation of the model architecture. In particular, we re-implemented the Attention Model and trained it with Proximal Policy Optimization (PPO) in CleanRL, showing at least 8 times speed up in training time. We hereby introduce RLOR, a flexible framework for Deep Reinforcement Learning for Operation Research. We believe that a flexible framework is key to developing deep reinforcement learning models for operation research problems. The code of our work is publicly available at https://github.com/cpwan/RLOR.

Large language models (LLMs) demonstrate remarkable capabilities, but their broad deployment is limited by significant computational resource demands, particularly energy consumption during inference. Static, one-model-fits-all inference strategies are often inefficient, as they do not exploit the diverse range of available models or adapt to varying query requirements. This paper presents GreenServ, a dynamic, context-aware routing framework that optimizes the trade-off between inference accuracy and energy efficiency. GreenServ extracts lightweight contextual features from each query, including task type, semantic cluster, and text complexity, and routes queries to the most suitable model from a heterogeneous pool, based on observed accuracy and energy usage. We employ a multi-armed bandit approach to learn adaptive routing policies online. This approach operates under partial feedback, eliminates the need for extensive offline calibration, and streamlines the integration of new models into the inference pipeline. We evaluated GreenServ across five benchmark tasks and a pool of 16 contemporary open-access LLMs. Experimental results show that GreenServ consistently outperforms static (single-model) and random baselines. In particular, compared to random routing, GreenServ achieved a 22% increase in accuracy while reducing cumulative energy consumption by 31%. Finally, we evaluated GreenServ with RouterBench, achieving an average accuracy of 71.7% with a peak accuracy of 75.7%. All artifacts are open-source and available here: https://github.com/TZData1/llm-inference-router{GitHub}

Today's LLM ecosystem comprises a wide spectrum of models that differ in size, capability, and cost. No single model is optimal for all scenarios; hence, LLM routers have become essential for selecting the most appropriate model under varying circumstances. However, the rapid emergence of various routers makes choosing the right one increasingly challenging. To address this problem, we need a comprehensive router comparison and a standardized leaderboard, similar to those available for models. In this work, we introduce RouterArena, the first open platform enabling comprehensive comparison of LLM routers. RouterArena has (1) a principally constructed dataset with broad knowledge domain coverage, (2) distinguishable difficulty levels for each domain, (3) an extensive list of evaluation metrics, and (4) an automated framework for leaderboard updates. Leveraging our framework, we have produced the initial leaderboard with detailed metrics comparison as shown in Figure 1. We will make our platform open to the public soon.

Combinatorial Optimization underpins many real-world applications and yet, designing performant algorithms to solve these complex, typically NP-hard, problems remains a significant research challenge. Reinforcement Learning (RL) provides a versatile framework for designing heuristics across a broad spectrum of problem domains. However, despite notable progress, RL has not yet supplanted industrial solvers as the go-to solution. Current approaches emphasize pre-training heuristics that construct solutions but often rely on search procedures with limited variance, such as stochastically sampling numerous solutions from a single policy or employing computationally expensive fine-tuning of the policy on individual problem instances. Building on the intuition that performant search at inference time should be anticipated during pre-training, we propose COMPASS, a novel RL approach that parameterizes a distribution of diverse and specialized policies conditioned on a continuous latent space. We evaluate COMPASS across three canonical problems - Travelling Salesman, Capacitated Vehicle Routing, and Job-Shop Scheduling - and demonstrate that our search strategy (i) outperforms state-of-the-art approaches on 11 standard benchmarking tasks and (ii) generalizes better, surpassing all other approaches on a set of 18 procedurally transformed instance distributions.

Many resource management problems require sequential decision-making under uncertainty, where the only uncertainty affecting the decision outcomes are exogenous variables outside the control of the decision-maker. We model these problems as Exo-MDPs (Markov Decision Processes with Exogenous Inputs) and design a class of data-efficient algorithms for them termed Hindsight Learning (HL). Our HL algorithms achieve data efficiency by leveraging a key insight: having samples of the exogenous variables, past decisions can be revisited in hindsight to infer counterfactual consequences that can accelerate policy improvements. We compare HL against classic baselines in the multi-secretary and airline revenue management problems. We also scale our algorithms to a business-critical cloud resource management problem -- allocating Virtual Machines (VMs) to physical machines, and simulate their performance with real datasets from a large public cloud provider. We find that HL algorithms outperform domain-specific heuristics, as well as state-of-the-art reinforcement learning methods.

Effective communication is key to successful, decentralized, multi-robot path planning. Yet, it is far from obvious what information is crucial to the task at hand, and how and when it must be shared among robots. To side-step these issues and move beyond hand-crafted heuristics, we propose a combined model that automatically synthesizes local communication and decision-making policies for robots navigating in constrained workspaces. Our architecture is composed of a convolutional neural network (CNN) that extracts adequate features from local observations, and a graph neural network (GNN) that communicates these features among robots. We train the model to imitate an expert algorithm, and use the resulting model online in decentralized planning involving only local communication and local observations. We evaluate our method in simulations {by navigating teams of robots to their destinations in 2D} cluttered workspaces. We measure the success rates and sum of costs over the planned paths. The results show a performance close to that of our expert algorithm, demonstrating the validity of our approach. In particular, we show our model's capability to generalize to previously unseen cases (involving larger environments and larger robot teams).

We propose a learning algorithm for local routing policies that needs only a few data samples obtained from a single graph while generalizing to all random graphs in a standard model of wireless networks. We thus solve the all-pairs near-shortest path problem by training deep neural networks (DNNs) that efficiently and scalably learn routing policies that are local, i.e., they only consider node states and the states of neighboring nodes. Remarkably, one of these DNNs we train learns a policy that exactly matches the performance of greedy forwarding; another generally outperforms greedy forwarding. Our algorithm design exploits network domain knowledge in several ways: First, in the selection of input features and, second, in the selection of a ``seed graph'' and subsamples from its shortest paths. The leverage of domain knowledge provides theoretical explainability of why the seed graph and node subsampling suffice for learning that is efficient, scalable, and generalizable. Simulation-based results on uniform random graphs with diverse sizes and densities empirically corroborate that using samples generated from a few routing paths in a modest-sized seed graph quickly learns a model that is generalizable across (almost) all random graphs in the wireless network model.

VRP (Vehicle Routing Problem) is an NP hard problem, and it has attracted a lot of research interest. In contexts where vehicles have limited carrying capacity, such as volume and weight but needed to deliver items at various locations. Initially before creating a route, each vehicle needs a group of delivery points that are not exceeding their maximum capacity. Drivers tend to deliver only to certain areas. Cluster-based is one of the approaches to give a basis for generating tighter routes. In this paper we propose new algorithms for producing such clusters/groups that do not exceed vehicles maximum capacity. Our basic assumptions are each vehicle originates from a depot, delivers the items to the customers and returns to the depot, also the vehicles are homogeneous. This methods are able to compact sub-areas in each cluster. Computational results demonstrate the effectiveness of our new procedures, which are able to assist users to plan service territories and vehicle routes more efficiently.

Autonomous driving is a key technology towards a brighter, more sustainable future. To enable such a future, it is necessary to utilize autonomous vehicles in shared mobility models. However, to evaluate, whether two or more route requests have the potential for a shared ride, is a compute-intensive task, if done by rerouting. In this work, we propose the Dynamic Longest Common Subsequences algorithm for fast and cost-efficient comparison of two routes for their compatibility, dynamically only incorporating parts of the routes which are suited for a shared trip. Based on this, one can also estimate, how many autonomous vehicles might be necessary to fulfill the local mobility demands. This can help providers to estimate the necessary fleet sizes, policymakers to better understand mobility patterns and cities to scale necessary infrastructure.

Existing methods usually leverage a fixed strategy, such as natural language reasoning, code-augmented reasoning, tool-integrated reasoning, or ensemble-based reasoning, to guide Large Language Models (LLMs) to perform mathematical reasoning. Our analysis reveals that the single strategy cannot adapt to problem-specific requirements and thus overlooks the trade-off between effectiveness and efficiency. To address these issues, we propose Planning and Routing through Instance-Specific Modeling (PRISM), a novel framework that decouples mathematical reasoning into two stages: strategy planning and targeted execution. Specifically, we first curate a multi-strategy preference dataset, which we call MathStrat, capturing correctness, process quality, and computational efficiency for each problem--strategy pair. Then, we train a lightweight Strategy Adapter based on the dataset to obtain confidence distributions over the mentioned four reasoning strategies. At inference time, an adaptive routing policy dynamically tailors the reasoning approach based on predictor confidence. It directs the model to use single-strategy execution for high-confidence predictions, dual-strategy verification for competitive scenarios, or comprehensive multi-strategy exploration for uncertain cases. Extensive experiments across five mathematical reasoning benchmarks demonstrate that PRISM consistently outperforms individual strategies and ensemble baselines, achieving improvements ranging from 0.9% to 7.6% across different base models. The adaptive routing approach shows particularly strong benefits for mathematical reasoning tasks across diverse model architectures. Our code is released at https://github.com/reml-group/PRISM.

Learning heuristics for vehicle routing problems (VRPs) has gained much attention due to the less reliance on hand-crafted rules. However, existing methods are typically trained and tested on the same task with a fixed size and distribution (of nodes), and hence suffer from limited generalization performance. This paper studies a challenging yet realistic setting, which considers generalization across both size and distribution in VRPs. We propose a generic meta-learning framework, which enables effective training of an initialized model with the capability of fast adaptation to new tasks during inference. We further develop a simple yet efficient approximation method to reduce the training overhead. Extensive experiments on both synthetic and benchmark instances of the traveling salesman problem (TSP) and capacitated vehicle routing problem (CVRP) demonstrate the effectiveness of our method. The code is available at: https://github.com/RoyalSkye/Omni-VRP.

This paper introduces RouteFinder, a comprehensive foundation model framework to tackle different Vehicle Routing Problem (VRP) variants. Our core idea is that a foundation model for VRPs should be able to represent variants by treating each as a subset of a generalized problem equipped with different attributes. We propose a unified VRP environment capable of efficiently handling any attribute combination. The RouteFinder model leverages a modern transformer-based encoder and global attribute embeddings to improve task representation. Additionally, we introduce two reinforcement learning techniques to enhance multi-task performance: mixed batch training, which enables training on different variants at once, and multi-variant reward normalization to balance different reward scales. Finally, we propose efficient adapter layers that enable fine-tuning for new variants with unseen attributes. Extensive experiments on 48 VRP variants show RouteFinder outperforms recent state-of-the-art learning methods. Code: https://github.com/ai4co/routefinder.

Multimodal recommendation enhances ranking by integrating user-item interactions with item content, which is particularly effective under sparse feedback and long-tail distributions. However, multimodal signals are inherently heterogeneous and can conflict in specific contexts, making effective fusion both crucial and challenging. Existing approaches often rely on shared fusion pathways, leading to entangled representations and modality imbalance. To address these issues, we propose MAGNET, a Modality-Guided Mixture of Adaptive Graph Experts Network with Progressive Entropy-Triggered Routing for Multimodal Recommendation, designed to enhance controllability, stability, and interpretability in multimodal fusion. MAGNET couples interaction-conditioned expert routing with structure-aware graph augmentation, so that both what to fuse and how to fuse are explicitly controlled and interpretable. At the representation level, a dual-view graph learning module augments the interaction graph with content-induced edges, improving coverage for sparse and long-tail items while preserving collaborative structure via parallel encoding and lightweight fusion. At the fusion level, MAGNET employs structured experts with explicit modality roles-dominant, balanced, and complementary-enabling a more interpretable and adaptive combination of behavioral, visual, and textual cues. To further stabilize sparse routing and prevent expert collapse, we introduce a two-stage entropy-weighting mechanism that monitors routing entropy. This mechanism automatically transitions training from an early coverage-oriented regime to a later specialization-oriented regime, progressively balancing expert utilization and routing confidence. Extensive experiments on public benchmarks demonstrate consistent improvements over strong baselines.

By routing input tokens to only a few split experts, Sparse Mixture-of-Experts has enabled efficient training of large language models. Recent findings suggest that fixing the routers can achieve competitive performance by alleviating the collapsing problem, where all experts eventually learn similar representations. However, this strategy has two key limitations: (i) the policy derived from random routers might be sub-optimal, and (ii) it requires extensive resources during training and evaluation, leading to limited efficiency gains. This work introduces \HyperRout, which dynamically generates the router's parameters through a fixed hypernetwork and trainable embeddings to achieve a balance between training the routers and freezing them to learn an improved routing policy. Extensive experiments across a wide range of tasks demonstrate the superior performance and efficiency gains of \HyperRouter compared to existing routing methods. Our implementation is publicly available at {{https://github.com/giangdip2410/HyperRouter}}.

In this paper we propose two algorithms in the tabular setting and an algorithm for the function approximation setting for the Stochastic Shortest Path (SSP) problem. SSP problems form an important class of problems in Reinforcement Learning (RL), as other types of cost-criteria in RL can be formulated in the setting of SSP. We show asymptotic almost-sure convergence for all our algorithms. We observe superior performance of our tabular algorithms compared to other well-known convergent RL algorithms. We further observe reliable performance of our function approximation algorithm compared to other algorithms in the function approximation setting.

In this paper, we explore the potential for quantum annealing to solve realistic routing problems. We focus on two NP-Hard problems, including the Traveling Salesman Problem with Time Windows and the Capacitated Vehicle Routing Problem with Time Windows. We utilize D-Wave's Quantum Annealer and Constrained Quadratic Model (CQM) solver within a hybrid framework to solve these problems. We demonstrate that while the CQM solver effectively minimizes route costs, it struggles to maintain time window feasibility as the problem size increases. To address this limitation, we implement a heuristic method that fixes infeasible solutions through a series of swapping operations. Testing on benchmark instances shows our method achieves promising results with an average optimality gap of 3.86%.

Vehicle-to-Vehicle (V2V) technologies have great potential for enhancing traffic flow efficiency and safety. However, cooperative decision-making in multi-agent systems, particularly in complex human-machine mixed merging areas, remains challenging for connected and autonomous vehicles (CAVs). Intent sharing, a key aspect of human coordination, may offer an effective solution to these decision-making problems, but its application in CAVs is under-explored. This paper presents an intent-sharing-based cooperative method, the Multi-Agent Proximal Policy Optimization with Prior Intent Sharing (MAPPO-PIS), which models the CAV cooperative decision-making problem as a Multi-Agent Reinforcement Learning (MARL) problem. It involves training and updating the agents' policies through the integration of two key modules: the Intention Generator Module (IGM) and the Safety Enhanced Module (SEM). The IGM is specifically crafted to generate and disseminate CAVs' intended trajectories spanning multiple future time-steps. On the other hand, the SEM serves a crucial role in assessing the safety of the decisions made and rectifying them if necessary. Merging area with human-machine mixed traffic flow is selected to validate our method. Results show that MAPPO-PIS significantly improves decision-making performance in multi-agent systems, surpassing state-of-the-art baselines in safety, efficiency, and overall traffic system performance. The code and video demo can be found at: https://github.com/CCCC1dhcgd/A-MAPPO-PIS.

Decision-focused learning (DFL) is an emerging paradigm that integrates machine learning (ML) and constrained optimization to enhance decision quality by training ML models in an end-to-end system. This approach shows significant potential to revolutionize combinatorial decision-making in real-world applications that operate under uncertainty, where estimating unknown parameters within decision models is a major challenge. This paper presents a comprehensive review of DFL, providing an in-depth analysis of both gradient-based and gradient-free techniques used to combine ML and constrained optimization. It evaluates the strengths and limitations of these techniques and includes an extensive empirical evaluation of eleven methods across seven problems. The survey also offers insights into recent advancements and future research directions in DFL. Code and benchmark: https://github.com/PredOpt/predopt-benchmarks

Increasing demand for Large Language Models (LLMs) services imposes substantial deployment and computation costs on providers. LLM routing offers a cost-efficient solution by directing queries to the optimal LLM based on model and query features. However, existing works primarily focus on offline scenarios and struggle to adapt to online settings with high query volume and constrained token budgets. In this work, we introduce the first training-free algorithm for online routing scenarios. Our algorithm leverages approximate nearest neighbor search to efficiently estimate query features and performs a one-time optimization over a small set of initial queries to learn a routing strategy that guides future routing. We provide theoretical guarantees demonstrating that our algorithm achieves a competitive ratio of 1 - o(1) under natural assumptions, which is further validated by extensive experiments across 3 benchmark datasets and 8 baselines, showing an average improvement of 3.55times in overall performance, 1.85times in cost efficiency, and nearly 4.25times in throughput. Our code is available at https://github.com/fzwark/PORT.

Prompt routing dynamically selects the most appropriate large language model from a pool of candidates for each query, optimizing performance while managing costs. As model pools scale to include dozens of frontier models with narrow performance gaps, existing approaches face significant challenges: manually defined task taxonomies cannot capture fine-grained capability distinctions, while monolithic routers struggle to differentiate subtle differences across diverse tasks. We propose a two-stage routing architecture that addresses these limitations through automated fine-grained task discovery and task-aware quality estimation. Our first stage employs graph-based clustering to discover latent task types and trains a classifier to assign prompts to discovered tasks. The second stage uses a mixture-of-experts architecture with task-specific prediction heads for specialized quality estimates. At inference, we aggregate predictions from both stages to balance task-level stability with prompt-specific adaptability. Evaluated on 10 benchmarks with 11 frontier models, our method consistently outperforms existing baselines and surpasses the strongest individual model while incurring less than half its cost.

The Multi-armed bandit offer the advantage to learn and exploit the already learnt knowledge at the same time. This capability allows this approach to be applied in different domains, going from clinical trials where the goal is investigating the effects of different experimental treatments while minimizing patient losses, to adaptive routing where the goal is to minimize the delays in a network. This article provides a review of the recent results on applying bandit to real-life scenario and summarize the state of the art for each of these fields. Different techniques has been proposed to solve this problem setting, like epsilon-greedy, Upper confident bound (UCB) and Thompson Sampling (TS). We are showing here how this algorithms were adapted to solve the different problems of exploration exploitation.

As the range of applications for Large Language Models (LLMs) continues to grow, the demand for effective serving solutions becomes increasingly critical. Despite the versatility of LLMs, no single model can optimally address all tasks and applications, particularly when balancing performance with cost. This limitation has led to the development of LLM routing systems, which combine the strengths of various models to overcome the constraints of individual LLMs. Yet, the absence of a standardized benchmark for evaluating the performance of LLM routers hinders progress in this area. To bridge this gap, we present RouterBench, a novel evaluation framework designed to systematically assess the efficacy of LLM routing systems, along with a comprehensive dataset comprising over 405k inference outcomes from representative LLMs to support the development of routing strategies. We further propose a theoretical framework for LLM routing, and deliver a comparative analysis of various routing approaches through RouterBench, highlighting their potentials and limitations within our evaluation framework. This work not only formalizes and advances the development of LLM routing systems but also sets a standard for their assessment, paving the way for more accessible and economically viable LLM deployments. The code and data are available at https://github.com/withmartian/routerbench.

Algorithms increasingly serve as information mediators--from social media feeds and targeted advertising to the increasing ubiquity of LLMs. This engenders a joint process where agents combine private, algorithmically-mediated signals with learning from peers to arrive at decisions. To study such settings, we introduce a model of controlled sequential social learning in which an information-mediating planner (e.g. an LLM) controls the information structure of agents while they also learn from the decisions of earlier agents. The planner may seek to improve social welfare (altruistic planner) or to induce a specific action the planner prefers (biased planner). Our framework presents a new optimization problem for social learning that combines dynamic programming with decentralized action choices and Bayesian belief updates. We prove the convexity of the value function and characterize the optimal policies of altruistic and biased planners, which attain desired tradeoffs between the costs they incur and the payoffs they earn from induced agent choices. Notably, in some regimes the biased planner intentionally obfuscates the agents' signals. Even under stringent transparency constraints--information parity with individuals, no lying or cherry-picking, and full observability--we show that information mediation can substantially shift social welfare in either direction. We complement our theory with simulations in which LLMs act as both planner and agents. Notably, the LLM planner in our simulations exhibits emergent strategic behavior in steering public opinion that broadly mirrors the trends predicted, though key deviations suggest the influence of non-Bayesian reasoning consistent with the cognitive patterns of both humans and LLMs trained on human-like data. Together, we establish our framework as a tractable basis for studying the impact and regulation of LLM information mediators.

A distribution shift can have fundamental consequences such as signaling a change in the operating environment or significantly reducing the accuracy of downstream models. Thus, understanding distribution shifts is critical for examining and hopefully mitigating the effect of such a shift. Most prior work focuses on merely detecting if a shift has occurred and assumes any detected shift can be understood and handled appropriately by a human operator. We hope to aid in these manual mitigation tasks by explaining the distribution shift using interpretable transportation maps from the original distribution to the shifted one. We derive our interpretable mappings from a relaxation of optimal transport, where the candidate mappings are restricted to a set of interpretable mappings. We then inspect multiple quintessential use-cases of distribution shift in real-world tabular, text, and image datasets to showcase how our explanatory mappings provide a better balance between detail and interpretability than baseline explanations by both visual inspection and our PercentExplained metric.

The availability of a wide range of large language models (LLMs) embedded in various agentic systems has significantly increased the potential of model selection strategies to improve the cost-performance tradeoff. Existing strategies involve either routing, where a single model is chosen per query, or cascading, which sequentially runs increasingly larger models until a satisfactory answer is found. However, current approaches face three key limitations: they (1) lack formal proofs of optimality, (2) fail to identify the conditions under which these strategies are most effective to improve the cost-performance tradeoff, and (3) are unable to combine both paradigms for further improvements. To address these issues, we first derive a novel optimal strategy for cascading and prove the optimality of an existing routing strategy. Further, we propose cascade routing, a unified framework that integrates routing and cascading into a theoretically optimal strategy. Through our analysis, we identify good quality estimators as the critical factor for the success of model selection paradigms. Finally, in our experiments, we show that cascade routing consistently outperforms the individual approaches by a large margin and we analyze quality estimators to determine when routing and/or cascading are useful paradigms for model selection.

Academic and policy proposals on algorithmic accountability often seek to understand algorithmic systems in their socio-technical context, recognising that they are produced by 'many hands'. Increasingly, however, algorithmic systems are also produced, deployed, and used within a supply chain comprising multiple actors tied together by flows of data between them. In such cases, it is the working together of an algorithmic supply chain of different actors who contribute to the production, deployment, use, and functionality that drives systems and produces particular outcomes. We argue that algorithmic accountability discussions must consider supply chains and the difficult implications they raise for the governance and accountability of algorithmic systems. In doing so, we explore algorithmic supply chains, locating them in their broader technical and political economic context and identifying some key features that should be understood in future work on algorithmic governance and accountability (particularly regarding general purpose AI services). To highlight ways forward and areas warranting attention, we further discuss some implications raised by supply chains: challenges for allocating accountability stemming from distributed responsibility for systems between actors, limited visibility due to the accountability horizon, service models of use and liability, and cross-border supply chains and regulatory arbitrage

We propose and evaluate a number of solutions to the problem of calculating the cost to serve each location in a single-vehicle transport setting. Such cost to serve analysis has application both strategically and operationally in transportation. The problem is formally given by the traveling salesperson game (TSG), a cooperative total utility game in which agents correspond to locations in a traveling salesperson problem (TSP). The cost to serve a location is an allocated portion of the cost of an optimal tour. The Shapley value is one of the most important normative division schemes in cooperative games, giving a principled and fair allocation both for the TSG and more generally. We consider a number of direct and sampling-based procedures for calculating the Shapley value, and present the first proof that approximating the Shapley value of the TSG within a constant factor is NP-hard. Treating the Shapley value as an ideal baseline allocation, we then develop six proxies for that value which are relatively easy to compute. We perform an experimental evaluation using Synthetic Euclidean games as well as games derived from real-world tours calculated for fast-moving consumer goods scenarios. Our experiments show that several computationally tractable allocation techniques correspond to good proxies for the Shapley value.

Reinforcement Learning (RL) has emerged as a powerful tool for neural combinatorial optimization, enabling models to learn heuristics that solve complex problems without requiring expert knowledge. Despite significant progress, existing RL approaches face challenges such as diminishing reward signals and inefficient exploration in vast combinatorial action spaces, leading to inefficiency. In this paper, we propose Preference Optimization, a novel method that transforms quantitative reward signals into qualitative preference signals via statistical comparison modeling, emphasizing the superiority among sampled solutions. Methodologically, by reparameterizing the reward function in terms of policy and utilizing preference models, we formulate an entropy-regularized RL objective that aligns the policy directly with preferences while avoiding intractable computations. Furthermore, we integrate local search techniques into the fine-tuning rather than post-processing to generate high-quality preference pairs, helping the policy escape local optima. Empirical results on various benchmarks, such as the Traveling Salesman Problem (TSP), the Capacitated Vehicle Routing Problem (CVRP) and the Flexible Flow Shop Problem (FFSP), demonstrate that our method significantly outperforms existing RL algorithms, achieving superior convergence efficiency and solution quality.

Continuous control tasks often involve high-dimensional, dynamic, and non-linear environments. State-of-the-art performance in these tasks is achieved through complex closed-box policies that are effective, but suffer from an inherent opacity. Interpretable policies, while generally underperforming compared to their closed-box counterparts, advantageously facilitate transparent decision-making within automated systems. Hence, their usage is often essential for diagnosing and mitigating errors, supporting ethical and legal accountability, and fostering trust among stakeholders. In this paper, we propose SMOSE, a novel method to train sparsely activated interpretable controllers, based on a top-1 Mixture-of-Experts architecture. SMOSE combines a set of interpretable decisionmakers, trained to be experts in different basic skills, and an interpretable router that assigns tasks among the experts. The training is carried out via state-of-the-art Reinforcement Learning algorithms, exploiting load-balancing techniques to ensure fair expert usage. We then distill decision trees from the weights of the router, significantly improving the ease of interpretation. We evaluate SMOSE on six benchmark environments from MuJoCo: our method outperforms recent interpretable baselines and narrows the gap with noninterpretable state-of-the-art algorithms

The profiled vehicle routing problem (PVRP) is a generalization of the heterogeneous capacitated vehicle routing problem (HCVRP) in which the objective is to optimize the routes of vehicles to serve client demands subject to different vehicle profiles, with each having a preference or constraint on a per-client basis. While existing learning methods have shown promise for solving the HCVRP in real-time, no learning method exists to solve the more practical and challenging PVRP. In this paper, we propose a Collaborative Attention Model with Profiles (CAMP), a novel approach that learns efficient solvers for PVRP using multi-agent reinforcement learning. CAMP employs a specialized attention-based encoder architecture to embed profiled client embeddings in parallel for each vehicle profile. We design a communication layer between agents for collaborative decision-making across profiled embeddings at each decoding step and a batched pointer mechanism to attend to the profiled embeddings to evaluate the likelihood of the next actions. We evaluate CAMP on two variants of PVRPs: PVRP with preferences, which explicitly influence the reward function, and PVRP with zone constraints with different numbers of agents and clients, demonstrating that our learned solvers achieve competitive results compared to both classical state-of-the-art neural multi-agent models in terms of solution quality and computational efficiency. We make our code openly available at https://github.com/ai4co/camp.

Large Language Models (LLMs) deliver state-of-the-art performance across many tasks but impose high computational and memory costs, limiting their deployment in resource-constrained or real-time settings. To address this, we propose HierRouter, a hierarchical routing approach that dynamically assembles inference pipelines from a pool of specialized, lightweight language models. Formulated as a finite-horizon Markov Decision Process (MDP), our approach trains a Proximal Policy Optimization (PPO)-based reinforcement learning agent to iteratively select which models to invoke at each stage of multi-hop inference. The agent conditions on the evolving context and accumulated cost to make context-aware routing decisions. Experiments with three open-source candidate LLMs across six benchmarks, including QA, code generation, and mathematical reasoning, show that HierRouter improves response quality by up to 2.4x compared to using individual models independently, while incurring only a minimal additional inference cost on average. These results highlight the promise of hierarchical routing for cost-efficient, high-performance LLM inference. All codes can be found here https://github.com/ Nikunj-Gupta/hierouter.

We present a fast algorithm for the design of smooth paths (or trajectories) that are constrained to lie in a collection of axis-aligned boxes. We consider the case where the number of these safe boxes is large, and basic preprocessing of them (such as finding their intersections) can be done offline. At runtime we quickly generate a smooth path between given initial and terminal positions. Our algorithm designs trajectories that are guaranteed to be safe at all times, and detects infeasibility whenever such a trajectory does not exist. Our algorithm is based on two subproblems that we can solve very efficiently: finding a shortest path in a weighted graph, and solving (multiple) convex optimal-control problems. We demonstrate the proposed path planner on large-scale numerical examples, and we provide an efficient open-source software implementation, fastpathplanning.

In this paper, we propose an autonomous information seeking visual question answering framework, AVIS. Our method leverages a Large Language Model (LLM) to dynamically strategize the utilization of external tools and to investigate their outputs, thereby acquiring the indispensable knowledge needed to provide answers to the posed questions. Responding to visual questions that necessitate external knowledge, such as "What event is commemorated by the building depicted in this image?", is a complex task. This task presents a combinatorial search space that demands a sequence of actions, including invoking APIs, analyzing their responses, and making informed decisions. We conduct a user study to collect a variety of instances of human decision-making when faced with this task. This data is then used to design a system comprised of three components: an LLM-powered planner that dynamically determines which tool to use next, an LLM-powered reasoner that analyzes and extracts key information from the tool outputs, and a working memory component that retains the acquired information throughout the process. The collected user behavior serves as a guide for our system in two key ways. First, we create a transition graph by analyzing the sequence of decisions made by users. This graph delineates distinct states and confines the set of actions available at each state. Second, we use examples of user decision-making to provide our LLM-powered planner and reasoner with relevant contextual instances, enhancing their capacity to make informed decisions. We show that AVIS achieves state-of-the-art results on knowledge-intensive visual question answering benchmarks such as Infoseek and OK-VQA.

The recently presented idea to learn heuristics for combinatorial optimization problems is promising as it can save costly development. However, to push this idea towards practical implementation, we need better models and better ways of training. We contribute in both directions: we propose a model based on attention layers with benefits over the Pointer Network and we show how to train this model using REINFORCE with a simple baseline based on a deterministic greedy rollout, which we find is more efficient than using a value function. We significantly improve over recent learned heuristics for the Travelling Salesman Problem (TSP), getting close to optimal results for problems up to 100 nodes. With the same hyperparameters, we learn strong heuristics for two variants of the Vehicle Routing Problem (VRP), the Orienteering Problem (OP) and (a stochastic variant of) the Prize Collecting TSP (PCTSP), outperforming a wide range of baselines and getting results close to highly optimized and specialized algorithms.

Multi-agent Pathfinding (MAPF) problem generally asks to find a set of conflict-free paths for a set of agents confined to a graph and is typically solved in a centralized fashion. Conversely, in this work, we investigate the decentralized MAPF setting, when the central controller that posses all the information on the agents' locations and goals is absent and the agents have to sequientially decide the actions on their own without having access to a full state of the environment. We focus on the practically important lifelong variant of MAPF, which involves continuously assigning new goals to the agents upon arrival to the previous ones. To address this complex problem, we propose a method that integrates two complementary approaches: planning with heuristic search and reinforcement learning through policy optimization. Planning is utilized to construct and re-plan individual paths. We enhance our planning algorithm with a dedicated technique tailored to avoid congestion and increase the throughput of the system. We employ reinforcement learning to discover the collision avoidance policies that effectively guide the agents along the paths. The policy is implemented as a neural network and is effectively trained without any reward-shaping or external guidance. We evaluate our method on a wide range of setups comparing it to the state-of-the-art solvers. The results show that our method consistently outperforms the learnable competitors, showing higher throughput and better ability to generalize to the maps that were unseen at the training stage. Moreover our solver outperforms a rule-based one in terms of throughput and is an order of magnitude faster than a state-of-the-art search-based solver.

Many cybersecurity problems that require real-time decision-making based on temporal observations can be abstracted as a sequence modeling problem, e.g., network intrusion detection from a sequence of arriving packets. Existing approaches like reinforcement learning may not be suitable for such cybersecurity decision problems, since the Markovian property may not necessarily hold and the underlying network states are often not observable. In this paper, we cast the problem of real-time network intrusion detection as casual sequence modeling and draw upon the power of the transformer architecture for real-time decision-making. By conditioning a causal decision transformer on past trajectories, consisting of the rewards, network packets, and detection decisions, our proposed framework will generate future detection decisions to achieve the desired return. It enables decision transformers to be applied to real-time network intrusion detection, as well as a novel tradeoff between the accuracy and timeliness of detection. The proposed solution is evaluated on public network intrusion detection datasets and outperforms several baseline algorithms using reinforcement learning and sequence modeling, in terms of detection accuracy and timeliness.

Route-planning agents powered by large language models (LLMs) have emerged as a promising paradigm for supporting everyday human mobility through natural language interaction and tool-mediated decision making. However, systematic evaluation in real-world mobility settings is hindered by diverse routing demands, non-deterministic mapping services, and limited reproducibility. In this study, we introduce MobilityBench, a scalable benchmark for evaluating LLM-based route-planning agents in real-world mobility scenarios. MobilityBench is constructed from large-scale, anonymized real user queries collected from Amap and covers a broad spectrum of route-planning intents across multiple cities worldwide. To enable reproducible, end-to-end evaluation, we design a deterministic API-replay sandbox that eliminates environmental variance from live services. We further propose a multi-dimensional evaluation protocol centered on outcome validity, complemented by assessments of instruction understanding, planning, tool use, and efficiency. Using MobilityBench, we evaluate multiple LLM-based route-planning agents across diverse real-world mobility scenarios and provide an in-depth analysis of their behaviors and performance. Our findings reveal that current models perform competently on Basic information retrieval and Route Planning tasks, yet struggle considerably with Preference-Constrained Route Planning, underscoring significant room for improvement in personalized mobility applications. We publicly release the benchmark data, evaluation toolkit, and documentation at https://github.com/AMAP-ML/MobilityBench .

In this paper, we introduce the Preselection Bandit problem, in which the learner preselects a subset of arms (choice alternatives) for a user, which then chooses the final arm from this subset. The learner is not aware of the user's preferences, but can learn them from observed choices. In our concrete setting, we allow these choices to be stochastic and model the user's actions by means of the Plackett-Luce model. The learner's main task is to preselect subsets that eventually lead to highly preferred choices. To formalize this goal, we introduce a reasonable notion of regret and derive lower bounds on the expected regret. Moreover, we propose algorithms for which the upper bound on expected regret matches the lower bound up to a logarithmic term of the time horizon.

We study the incentivized information acquisition problem, where a principal hires an agent to gather information on her behalf. Such a problem is modeled as a Stackelberg game between the principal and the agent, where the principal announces a scoring rule that specifies the payment, and then the agent then chooses an effort level that maximizes her own profit and reports the information. We study the online setting of such a problem from the principal's perspective, i.e., designing the optimal scoring rule by repeatedly interacting with the strategic agent. We design a provably sample efficient algorithm that tailors the UCB algorithm (Auer et al., 2002) to our model, which achieves a sublinear T^{2/3}-regret after T iterations. Our algorithm features a delicate estimation procedure for the optimal profit of the principal, and a conservative correction scheme that ensures the desired agent's actions are incentivized. Furthermore, a key feature of our regret bound is that it is independent of the number of states of the environment.

As large language models (LLMs) grow in scale and specialization, routing--selecting the best model for a given input--has become essential for efficient and effective deployment. While recent methods rely on complex learned routing strategies, their dependence on disparate training data and evaluation setups makes comparison and generalization difficult. In this work, we revisit LLM routing through the lens of simplicity. We show that a well-tuned k-Nearest Neighbors (kNN) approach not only matches but often outperforms state-of-the-art learned routers across diverse tasks. To support systematic evaluation, we introduce a suite of standardized routing benchmarks spanning instruction-following, question-answering, and reasoning tasks, as well as the first multi-modal routing dataset involving visual inputs. Our findings reveal that the locality properties of model performance in embedding space enable simple non-parametric methods to achieve strong routing decisions with lower sample complexity than parametric approaches. This challenges the prevailing trend toward sophisticated architectures and highlights the importance of thoroughly evaluating simple baselines before investing in complex solutions. To support reproducibility and further exploration, we will release all benchmarks and code upon publication.

Pre-routing slack prediction remains a critical area of research in Electronic Design Automation (EDA). Despite numerous machine learning-based approaches targeting this task, there is still a lack of a truly end-to-end framework that engineers can use to obtain TNS/WNS metrics from raw circuit data at the placement stage. Existing works have demonstrated effectiveness in Arrival Time (AT) prediction but lack a mechanism for Required Arrival Time (RAT) prediction, which is essential for slack prediction and obtaining TNS/WNS metrics. In this work, we propose E2ESlack, an end-to-end graph-based framework for pre-routing slack prediction. The framework includes a TimingParser that supports DEF, SDF and LIB files for feature extraction and graph construction, an arrival time prediction model and a fast RAT estimation module. To the best of our knowledge, this is the first work capable of predicting path-level slacks at the pre-routing stage. We perform extensive experiments and demonstrate that our proposed RAT estimation method outperforms the SOTA ML-based prediction method and also pre-routing STA tool. Additionally, the proposed E2ESlack framework achieves TNS/WNS values comparable to post-routing STA results while saving up to 23x runtime.

In this paper, we present Batch Informed Trees (BIT*), a planning algorithm based on unifying graph- and sampling-based planning techniques. By recognizing that a set of samples describes an implicit random geometric graph (RGG), we are able to combine the efficient ordered nature of graph-based techniques, such as A*, with the anytime scalability of sampling-based algorithms, such as Rapidly-exploring Random Trees (RRT). BIT* uses a heuristic to efficiently search a series of increasingly dense implicit RGGs while reusing previous information. It can be viewed as an extension of incremental graph-search techniques, such as Lifelong Planning A* (LPA*), to continuous problem domains as well as a generalization of existing sampling-based optimal planners. It is shown that it is probabilistically complete and asymptotically optimal. We demonstrate the utility of BIT* on simulated random worlds in R^2 and R^8 and manipulation problems on CMU's HERB, a 14-DOF two-armed robot. On these problems, BIT* finds better solutions faster than RRT, RRT*, Informed RRT*, and Fast Marching Trees (FMT*) with faster anytime convergence towards the optimum, especially in high dimensions.

Diffusion language models (DLMs) enable parallel, non-autoregressive text generation, yet existing DLM mixture-of-experts (MoE) models inherit token-choice (TC) routing from autoregressive systems, leading to load imbalance and rigid computation allocation. We show that expert-choice (EC) routing is a better fit for DLMs: it provides deterministic load balancing by design, yielding higher throughput and faster convergence than TC. Building on the property that EC capacity is externally controllable, we introduce timestep-dependent expert capacity, which varies expert allocation according to the denoising step. We find that allocating more capacity to low-mask-ratio steps consistently achieves the best performance under matched FLOPs, and provide a mechanistic explanation: tokens in low-mask-ratio contexts exhibit an order-of-magnitude higher learning efficiency, so concentrating compute on these steps yields the largest marginal return. Finally, we show that existing pretrained TC DLMs can be retrofitted to EC by replacing only the router, achieving faster convergence and improved accuracy across diverse downstream tasks. Together, these results establish EC routing as a superior paradigm for DLM MoE models and demonstrate that computation in DLMs can be treated as an adaptive policy rather than a fixed architectural constant. Code is available at https://github.com/zhangshuibai/EC-DLM.

We introduce directional routing, a lightweight mechanism that gives each transformer attention head learned suppression directions controlled by a shared router, at 3.9% parameter cost. We train a 433M-parameter model alongside an identical baseline in a single run, then trace the resulting circuits through mechanistic interpretability. Routing becomes the model's dominant computational pathway. Disabling it collapses factual recall to near-zero probability across all 8 test prompts and drops induction accuracy from 93.4% to 0.0%. Knocking out individual attention heads has negligible effect: the primary mover head's removal actually increases target probability, and induction heads retain 98.6% accuracy without their strongest member. The coordination mechanism is irreplaceable; the components it coordinates are not. The model also self-organizes, without explicit pressure, into two regimes: domain-adaptive routing in early layers and fixed syntactic pruning in late layers, where the least-varying layer is the most critical (+42.6 PPL when disabled). Routing reduces perplexity 31-56% relative to the baseline, though downstream multiple-choice benchmarks do not yet reflect these gains.

Modeling networks as different graph types and researching on route finding strategies, to avoid congestion in dense subnetworks via graph-theoretic approaches, contributes to overall blocking probability reduction in networks. Our main focus is to study methods for modeling congested subnetworks and graph density measures, in order to identify routes that avoid dense subgraphs for global congestion avoidance, along with covering related algorithmic issues.

Information is often stored in a distributed and proprietary form, and agents who own information are often self-interested and require incentives to reveal their information. Suitable mechanisms are required to elicit and aggregate such distributed information for decision making. In this paper, we use simulations to investigate the use of decision markets as mechanisms in a multi-agent learning system to aggregate distributed information for decision-making in a contextual bandit problem. The system utilises strictly proper decision scoring rules to assess the accuracy of probabilistic reports from agents, which allows agents to learn to solve the contextual bandit problem jointly. Our simulations show that our multi-agent system with distributed information can be trained as efficiently as a centralised counterpart with a single agent that receives all information. Moreover, we use our system to investigate scenarios with deterministic decision scoring rules which are not incentive compatible. We observe the emergence of more complex dynamics with manipulative behaviour, which agrees with existing theoretical analyses.

The proposed IncidentResponseGPT framework - a novel system that applies generative artificial intelligence (AI) to potentially enhance the efficiency and effectiveness of traffic incident response. This model allows for synthesis of region-specific incident response guidelines and generates incident response plans adapted to specific area, aiming to expedite decision-making for traffic management authorities. This approach aims to accelerate incident resolution times by suggesting various recommendations (e.g. optimal rerouting strategies, estimating resource needs) to minimize the overall impact on the urban traffic network. The system suggests specific actions, including dynamic lane closures, optimized rerouting and dispatching appropriate emergency resources. IncidentResponseGPT employs the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to rank generated response plans based on criteria like impact minimization and resource efficiency based on their proximity to an human-proposed solution.

In large-scale AI training, Sparse Mixture-of-Experts (s-MoE) layers enable scaling by activating only a small subset of experts per token. An operational challenge in this design is load balancing: routing tokens to minimize the number of idle experts, which is important for the efficient utilization of (costly) GPUs. We provide a theoretical framework for analyzing the Auxiliary-Loss-Free Load Balancing (ALF-LB) procedure -- proposed by DeepSeek's Wang et al. (2024) -- by casting it as a one-step-per-iteration primal-dual method for an assignment problem. First, in a stylized deterministic setting, our framework yields several insightful structural properties: (i) a monotonic improvement of a Lagrangian objective, (ii) a preference rule that moves tokens from overloaded to underloaded experts, and (iii) an approximate-balancing guarantee. Then, we incorporate the stochastic and dynamic nature of AI training using a generalized online optimization formulation. In the online setting, we derive a strong convexity property of the objective that leads to a logarithmic expected regret bound under certain step-size choices. Additionally, we present real experiments on 1B-parameter DeepSeekMoE models to complement our theoretical findings. Together, these results build a principled framework for analyzing the Auxiliary-Loss-Free Load Balancing of s-MoE in AI models.

This study addresses challenges in reverse logistics, a frequently overlooked but essential component of last-mile delivery, particularly in disaster relief scenarios where infrastructure disruptions demand adaptive solutions. While hub-and-spoke logistics networks excel at long-distance scalability, they often fail to optimize closely spaced spokes reliant on distant hubs, introducing inefficiencies in transit times and resource allocation. Using 20 Apple AirTags embedded in packages, this research provides empirical insights into logistical flows, capturing granular spatial and temporal data through Bluetooth LE (BLE) 5 trackers integrated with the Apple Find My network. These trackers demonstrated their value in monitoring dynamic cargo movements, enabling real-time adjustments in mobile hub placement and route optimization, particularly in disaster relief contexts like Hurricane Helene. A novel application of discrete event simulation (DES) further explored the saddle point in hub-spoke configurations, where excessive hub reliance clashes with diminishing spoke interaction demand. By coupling simulation results with empirical AirTag tracking, the study highlights the potential of BLE technology to refine reverse logistics, reduce delays, and improve operational flexibility in both routine and crisis-driven delivery networks.

In their seminal work, Nayyar et al. (2013) showed that imperfect information can be abstracted away from common-payoff games by having players publicly announce their policies as they play. This insight underpins sound solvers and decision-time planning algorithms for common-payoff games. Unfortunately, a naive application of the same insight to two-player zero-sum games fails because Nash equilibria of the game with public policy announcements may not correspond to Nash equilibria of the original game. As a consequence, existing sound decision-time planning algorithms require complicated additional mechanisms that have unappealing properties. The main contribution of this work is showing that certain regularized equilibria do not possess the aforementioned non-correspondence problem -- thus, computing them can be treated as perfect-information problems. Because these regularized equilibria can be made arbitrarily close to Nash equilibria, our result opens the door to a new perspective to solving two-player zero-sum games and yields a simplified framework for decision-time planning in two-player zero-sum games, void of the unappealing properties that plague existing decision-time planning approaches.

Stochastic optimization is one of the central problems in Machine Learning and Theoretical Computer Science. In the standard model, the algorithm is given a fixed distribution known in advance. In practice though, one may acquire at a cost extra information to make better decisions. In this paper, we study how to buy information for stochastic optimization and formulate this question as an online learning problem. Assuming the learner has an oracle for the original optimization problem, we design a 2-competitive deterministic algorithm and a e/(e-1)-competitive randomized algorithm for buying information. We show that this ratio is tight as the problem is equivalent to a robust generalization of the ski-rental problem, which we call super-martingale stopping. We also consider an adaptive setting where the learner can choose to buy information after taking some actions for the underlying optimization problem. We focus on the classic optimization problem, Min-Sum Set Cover, where the goal is to quickly find an action that covers a given request drawn from a known distribution. We provide an 8-competitive algorithm running in polynomial time that chooses actions and decides when to buy information about the underlying request.

We study the problem of learning in the stochastic shortest path (SSP) setting, where an agent seeks to minimize the expected cost accumulated before reaching a goal state. We design a novel model-based algorithm EB-SSP that carefully skews the empirical transitions and perturbs the empirical costs with an exploration bonus to induce an optimistic SSP problem whose associated value iteration scheme is guaranteed to converge. We prove that EB-SSP achieves the minimax regret rate O(B_{star} S A K), where K is the number of episodes, S is the number of states, A is the number of actions, and B_{star} bounds the expected cumulative cost of the optimal policy from any state, thus closing the gap with the lower bound. Interestingly, EB-SSP obtains this result while being parameter-free, i.e., it does not require any prior knowledge of B_{star}, nor of T_{star}, which bounds the expected time-to-goal of the optimal policy from any state. Furthermore, we illustrate various cases (e.g., positive costs, or general costs when an order-accurate estimate of T_{star} is available) where the regret only contains a logarithmic dependence on T_{star}, thus yielding the first (nearly) horizon-free regret bound beyond the finite-horizon MDP setting.

To optimally coordinate with others in cooperative games, it is often crucial to have information about one's collaborators: successful driving requires understanding which side of the road to drive on. However, not every feature of collaborators is strategically relevant: the fine-grained acceleration of drivers may be ignored while maintaining optimal coordination. We show that there is a well-defined dichotomy between strategically relevant and irrelevant information. Moreover, we show that, in dynamic games, this dichotomy has a compact representation that can be efficiently computed via a Bellman backup operator. We apply this algorithm to analyze the strategically relevant information for tasks in both a standard and a partially observable version of the Overcooked environment. Theoretical and empirical results show that our algorithms are significantly more efficient than baselines. Videos are available at https://minknowledge.github.io.

We consider a class of assortment optimization problems in an offline data-driven setting. A firm does not know the underlying customer choice model but has access to an offline dataset consisting of the historically offered assortment set, customer choice, and revenue. The objective is to use the offline dataset to find an optimal assortment. Due to the combinatorial nature of assortment optimization, the problem of insufficient data coverage is likely to occur in the offline dataset. Therefore, designing a provably efficient offline learning algorithm becomes a significant challenge. To this end, we propose an algorithm referred to as Pessimistic ASsortment opTimizAtion (PASTA for short) designed based on the principle of pessimism, that can correctly identify the optimal assortment by only requiring the offline data to cover the optimal assortment under general settings. In particular, we establish a regret bound for the offline assortment optimization problem under the celebrated multinomial logit model. We also propose an efficient computational procedure to solve our pessimistic assortment optimization problem. Numerical studies demonstrate the superiority of the proposed method over the existing baseline method.

Smart cities will be characterized by a variety of intelligent and networked services, each with specific requirements for the underlying network infrastructure. While smart city architectures and services have been studied extensively, little attention has been paid to the network technology. The KIGLIS research project, consisting of a consortium of companies, universities and research institutions, focuses on artificial intelligence for optimizing fiber-optic networks of a smart city, with a special focus on future mobility applications, such as automated driving. In this paper, we present early results on our process of collecting smart city requirements for communication networks, which will lead towards reference infrastructure and architecture solutions. Finally, we suggest directions in which artificial intelligence will improve smart city networks.

We introduce a new balanced assignment of experts (BASE) layer for large language models that greatly simplifies existing high capacity sparse layers. Sparse layers can dramatically improve the efficiency of training and inference by routing each token to specialized expert modules that contain only a small fraction of the model parameters. However, it can be difficult to learn balanced routing functions that make full use of the available experts; existing approaches typically use routing heuristics or auxiliary expert-balancing loss functions. In contrast, we formulate token-to-expert allocation as a linear assignment problem, allowing an optimal assignment in which each expert receives an equal number of tokens. This optimal assignment scheme improves efficiency by guaranteeing balanced compute loads, and also simplifies training by not requiring any new hyperparameters or auxiliary losses. Code is publicly released at https://github.com/pytorch/fairseq/

While Large Language Models (LLMs) have recently shown promise in Automated Heuristic Design (AHD), existing approaches typically formulate AHD around constructive priority rules or parameterized local search guidance, thereby restricting the search space to fixed heuristic forms. Such designs offer limited capacity for structural exploration, making it difficult to escape deep local optima in complex Combinatorial Optimization Problems (COPs). In this work, we propose G-LNS, a generative evolutionary framework that extends LLM-based AHD to the automated design of Large Neighborhood Search (LNS) operators. Unlike prior methods that evolve heuristics in isolation, G-LNS leverages LLMs to co-evolve tightly coupled pairs of destroy and repair operators. A cooperative evaluation mechanism explicitly captures their interaction, enabling the discovery of complementary operator logic that jointly performs effective structural disruption and reconstruction. Extensive experiments on challenging COP benchmarks, such as Traveling Salesman Problems (TSP) and Capacitated Vehicle Routing Problems (CVRP), demonstrate that G-LNS significantly outperforms LLM-based AHD methods as well as strong classical solvers. The discovered heuristics not only achieve near-optimal solutions with reduced computational budgets but also exhibit robust generalization across diverse and unseen instance distributions.

Mixture of Experts (MoE) has become a key ingredient for scaling large foundation models while keeping inference costs steady. We show that expert routing strategies that have cross-batch dependencies are vulnerable to attacks. Malicious queries can be sent to a model and can affect a model's output on other benign queries if they are grouped in the same batch. We demonstrate this via a proof-of-concept attack in a toy experimental setting.

We investigate the mechanism design problem faced by a principal who hires multiple agents to gather and report costly information. Then, the principal exploits the information to make an informed decision. We model this problem as a game, where the principal announces a mechanism consisting in action recommendations and a payment function, a.k.a. scoring rule. Then, each agent chooses an effort level and receives partial information about an underlying state of nature based on the effort. Finally, the agents report the information (possibly non-truthfully), the principal takes a decision based on this information, and the agents are paid according to the scoring rule. While previous work focuses on single-agent problems, we consider multi-agents settings. This poses the challenge of coordinating the agents' efforts and aggregating correlated information. Indeed, we show that optimal mechanisms must correlate agents' efforts, which introduces externalities among the agents, and hence complex incentive compatibility constraints and equilibrium selection problems. First, we design a polynomial-time algorithm to find an optimal incentive compatible mechanism. Then, we study an online problem, where the principal repeatedly interacts with a group of unknown agents. We design a no-regret algorithm that provides mathcal{O}(T^{2/3}) regret with respect to an optimal mechanism, matching the state-of-the-art bound for single-agent settings.

Evaluating production LLM responses and routing requests across providers in LLM gateways requires fine-grained quality signals and operationally grounded decisions. To address this gap, we present SEAR, a schema-based evaluation and routing system for multi-model, multi-provider LLM gateways. SEAR defines an extensible relational schema covering both LLM evaluation signals (context, intent, response characteristics, issue attribution, and quality scores) and gateway operational metrics (latency, cost, throughput), with cross-table consistency links across around one hundred typed, SQL-queryable columns. To populate the evaluation signals reliably, SEAR proposes self-contained signal instructions, in-schema reasoning, and multi-stage generation that produces database-ready structured outputs. Because signals are derived through LLM reasoning rather than shallow classifiers, SEAR captures complex request semantics, enables human-interpretable routing explanations, and unifies evaluation and routing in a single query layer. Across thousands of production sessions, SEAR achieves strong signal accuracy on human-labeled data and supports practical routing decisions, including large cost reductions with comparable quality.