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| "text": "Data-Efficient Hierarchical Reinforcement Learning Ofir Nachum Shixiang Gu∗\nGoogle Brain Google Brain\nofirnachum@google.com shanegu@google.com Honglak Lee Sergey Levine†\nGoogle Brain Google Brain\nhonglak@google.com slevine@google.com2018 AbstractOct\n5 Hierarchical reinforcement learning (HRL) is a promising approach to extend\ntraditional reinforcement learning (RL) methods to solve more complex tasks. Yet, the majority of current HRL methods require careful task-specific design and\non-policy training, making them difficult to apply in real-world scenarios. In this\npaper, we study how we can develop HRL algorithms that are general, in that they\ndo not make onerous additional assumptions beyond standard RL algorithms, and\nefficient, in the sense that they can be used with modest numbers of interaction[cs.LG] samples, making them suitable for real-world problems such as robotic control. For\ngenerality, we develop a scheme where lower-level controllers are supervised with\ngoals that are learned and proposed automatically by the higher-level controllers. To address efficiency, we propose to use off-policy experience for both higherand lower-level training. This poses a considerable challenge, since changes to\nthe lower-level behaviors change the action space for the higher-level policy, and\nwe introduce an off-policy correction to remedy this challenge. This allows us\nto take advantage of recent advances in off-policy model-free RL to learn both\nhigher- and lower-level policies using substantially fewer environment interactions\nthan on-policy algorithms. We term the resulting HRL agent HIRO and find that\nit is generally applicable and highly sample-efficient. Our experiments show that\nHIRO can be used to learn highly complex behaviors for simulated robots, such\nas pushing objects and utilizing them to reach target locations,1 learning from\nonly a few million samples, equivalent to a few days of real-time interaction. In\ncomparisons with a number of prior HRL methods, we find that our approach Deep reinforcement learning (RL) has made significant progress on a range of continuous control\ntasks, such as locomotion skills [39, 27, 18], learning dexterous manipulation behaviors [36], and\ntraining robot arms for simple manipulation tasks [13, 46]. However, most of these behaviors are\ninherently atomic: they require performing some simple skill, either episodically or cyclically, and\nrarely involve complex multi-level reasoning, such as utilizing a variety of locomotion behaviors to\naccomplish complex goals that require movement, object interaction, and discrete decision-making.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "∗Also at University of Cambridge; Max Planck Institute of Intelligent Systems.\n†Also at UC Berkeley.\n1See videos at https://sites.google.com/view/efficient-hrl\n2Find open-source code at https://github.com/tensorflow/models/tree/master/research/\nefficient-hrl 32nd Conference on Neural Information Processing Systems (NIPS 2018), Montréal, Canada. Figure 1: The Ant Gather task along with the three hierarchical navigation tasks we consider:\nAnt Maze, Ant Push, and Ant Fall. The ant (magenta rectangle) is rewarded for approaching the\ntarget location (green arrow).", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "A successful policy must perform a complex sequence of directional\nmovement and, in some cases, interact with objects in its environment (red blocks); e.g., pushing aside\nan obstacle (second from right) or using a block as a bridge (right). In our HRL method, a higher-level\npolicy periodically produces goal states (corresponding to desired positions and orientations of the\nant and its limbs), which the lower-level policy is rewarded to match (blue arrow). Hierarchical reinforcement learning (HRL), in which multiple layers of policies are trained to perform\ndecision-making and control at successively higher levels of temporal and behavioral abstraction, has\nlong held the promise to learn such difficult tasks [7, 32, 43, 4]. By having a hierarchy of policies,\nof which only the lowest applies actions to the environment, one is able to train the higher levels\nto plan over a longer time scale. Moreover, if the high-level actions correspond to semantically\ndifferent low-level behavior, standard exploration techniques may be applied to more appropriately\nexplore a complex environment. Still, there is a large gap between the basic definition of HRL\nand the promise it holds to successfully solve complex environments. To achieve the benefits of\nHRL, there are a number of questions that one must suitably answer: How should one train the\nlower-level policy to induce semantically distinct behavior? How should the high-level policy actions\nbe defined? How should the multiple policies be trained without incurring an inordinate amount\nof experience collection?", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
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| "text": "Previous work has attempted to answer these questions in a variety of\nways and has provided encouraging successes [48, 10, 11, 19, 40]. However, many of these methods\nlack generality, requiring some degree of manual task-specific design, and often require expensive\non-policy training that is unable to benefit from advances in off-policy model-free RL, which in\nrecent years has drastically brought down sample complexity requirements [12, 16, 3]. For generality, we propose to take advantage of the state observation provided by the environment\nto the agent, which in locomotion tasks can include the position and orientation of the agent and its\nlimbs. We let the high-level actions be goal states and reward the lower-level policy for performing\nactions which yield it an observation close to matching the desired goal. In this way, our HRL setup\ndoes not require a manual or multi-task design and is fully general.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "This idea of a higher-level policy commanding a lower-level policy to match observations to a goal\nstate has been proposed before [7, 48]. Unlike previous work, which represented goals and rewarded\nmatching observations within a learned embedding space, we use the state observations in their\nraw form. This significantly simplifies the learning, and in our experiments, we observe substantial\nbenefits for this simpler approach. While these goal-proposing methods are very general, they require training with on-policy RL\nalgorithms, which are generally less efficient than off-policy methods [15, 31]. On-policy training\nhas been attractive in the past since, outside of discrete control, off-policy methods have been plagued\nwith instability [15], which is amplified when training multiple policies jointly, as in HRL. Other than\ninstability, off-policy training poses another challenge that is unique to HRL. Since the lower-level\npolicy is changing underneath the higher-level policy, a sample observed for a certain high-level\naction in the past may not yield the same low-level behavior in the future, and thus not be a valid\nexperience for training. This amounts to a non-stationary problem for the higher-level policy. We\nremedy this issue by introducing an off-policy correction, which re-labels an experience in the past\nwith a high-level action chosen to maximize the probability of the past lower-level actions. In this way,\nwe are able to use past experience for training the higher-level policy, taking advantage of progress\nmade in recent years to provide stable, robust, and general off-policy RL methods [12, 31, 3]. In summary, we introduce a method to train a multi-level HRL agent that stands out from previous\nmethods by being both generally applicable and data-efficient. Our method achieves generality by\ntraining the lower-level policy to reach goal states learned and instructed by the higher-levels. In\ncontrast to prior work that operates in this goal-setting model, we use states as goals directly, which\nallows for simple and fast training of the lower layer. Moreover, by using off-policy training with our novel off-policy correction, our method is extremely sample-efficient.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
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| "text": "We evaluate our method\non several difficult environments. These environments require the ability to perform exploratory\nnavigation as well as complex sequences of interaction with objects in the environment (see Figure 1). While these tasks are unsolvable by existing non-HRL methods, we find that our HRL setup can\nlearn successful policies. When compared to other published HRL methods, we also observe the\nsuperiority of our method, in terms of both final performance and speed of learning. In only a few\nmillion experience samples, our agents are able to adequately solve previously unapproachable tasks.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
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| "text": "We adopt the standard continuous control RL setting, in which an agent interacts with an environment\nover periods of time according to a behavior policy µ. At each time step t, the environment produces\na state observation st ∈Rds.The agent then samples an action at ∼µ(st), at ∈Rdaand applies\nthe action to the environment. The environment then yields a reward Rt sampled from an unknown\nreward function R(st, at) and either terminates the episode at state sT or transitions to a new state\nst+1 sampled from an unknown transition function f(st, at). The agent's goal is to maximize the\nexpected future discounted reward Es0:T ,a0:T −1,R0:T −1 hPTi=0−1 γiRi i , where 0 ≤γ < 1 is a userspecified discount factor. A well-performing RL algorithm will learn a good behavior policy µ from\n(ideally a small number of) interactions with the environment. 2.1 Off-Policy Temporal Difference Learning Temporal difference learning is a powerful paradigm in RL, in which a policy may be learned\nefficiently from state-action-reward transition tuples (st, at, Rt, st+1) collected from interactions\nwith the environment. In our HRL method, we utilize the TD3 learning algorithm [12], a variant of\nthe popular DDPG algorithm for continuous control [27]. In DDPG, a deterministic neural network policy µφ is learned along with its corresponding stateaction Q-function Qθ by performing gradient updates on parameter sets φ and θ. The Q-function\nrepresents the future value of taking a specific action at starting from a state st. Accordingly, it is\ntrained to minimize the average Bellman error over all sampled transitions, which is given by\nE(st, at, st+1) = (Qθ(st, at) −Rt −γQθ(st+1, µφ(st+1)))2. (1) The policy is then trained to yield actions which maximize the Q-value at each state. That is, µφ is\ntrained to maximize Qθ(st, µφ(st)) over all st collected from interactions with the environment. We note that although DDPG trains a deterministic policy µφ, its behavior policy, which is used to\ncollect experience during training is augmented with Gaussian (or Ornstein-Uhlenbeck) noise [27]. Therefore, actions are collected as at ∼N(µφ(st), σ) for fixed standard deviation σ, which we will\nshorten as at ∼µφ(st).", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "We will take advantage of the fact that the behavior policy is stochastic for\nthe off-policy correction in our HRL method. TD3 [12] makes several modifications to DDPG's\nlearning algorithm to yield a more robust and stable procedure. Its main modification is using an\nensemble over Q-value models and adding noise to the policy when computing the target value in\nEquation 1. 3 General and Efficient Hierarchical Reinforcement Learning In this section, we present our framework for learning hierarchical policies, HIRO: HIerarchical\nReinforcement learning with Off-policy correction. We make use of parameterized reward functions\nto specify a potentially infinite set of lower-level policies, each of which is trained to match its\nobserved states st to a desired goal. The higher-level policy chooses these goals for temporally\nextended periods, and uses an off-policy correction to enable it to use past experience collected from\nprevious, different instantiations of the lower-level policy. 3.1 Hierarchy of Two Policies We extend the standard RL setup to a hierarchical two-layer structure, with a lower-level policy\nµlo and a higher-level policy µhi (see Figure 2). The higher-level policy operates at a coarser layer Collect experience st, gt, at, Rt, . . . . Train with experience transitions g0 h g1 . . . h gc - 1 gc using (st, gt, at, rt, st+1, gt+1) gt as\nadditional state observation and reward given by rewards r(st, gt, at, st+1). r(st, gt, at, st+1) = −||st + gt −st+1||2. μlo μlo . . . μlo μlo respectOff-policyto goal-conditionedtraining with goal-conditioned function rt =\ns0 s1 sc - 1 sc\na0 a1 ac - 1 ac 3. Train µhi on temporally-extended experience\nPrincipled off-policy\ntraining with goal (st, ˜gt, P Rt:t+c−1, st+c), where ˜gt is rere-labelling. labelled high-level action to maximize probability Environment . . .\nof past low-level actions at:t+c−1. Figure 2: The design and basic training of HIRO.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
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| "text": "The lower-level policy interacts directly with the\nenvironment. The higher-level policy instructs the lower-level policy via high-level actions, or goals,\ngt ∈Rds which it samples anew every c steps. On intermediate steps, a fixed goal transition function\nh determines the next step's goal. The goal simply instructs the lower-level policy to reach specific\nstates, which allows the lower-level policy to easily learn from prior off-policy experience. Figure 3: An example of a higher-level policy producing goals in terms of desired observations,\nwhich in this task correspond to positions and orientations of all of the joints of a quadrupedal robot\n(including root position). The lower-level policy has direct control of the agent (pink), and is rewarded\nfor matching the position and orientation of its torso and each limb to the goal (blue rectangle, raised\nfor visibility). In this way, the two-layer policy can perform a complex task involving a sequence of\nmovements and interactions; e.g. pushing a block aside to reach a target (green). of abstraction and sets goals to the lower-level policy, which correspond directly to states that the\nlower-level policy attempts to reach. At each time step t, the environment provides an observation\nstate st. The higher-level policy observes the state and produces a high-level action (or goal) gt ∈Rds\nby either sampling from its policy gt ∼µhi when t ≡0 (mod c), or otherwise using a fixed goal\ntransition function gt = h(st−1, gt−1, st) (which in the simplest case can be a pass-through function,\nalthough we will consider a slight variation in our specific design). This provides temporal abstraction,\nsince high-level decisions via µhi are made only every c steps. The lower-level policy µlo observes\nthe state st and goal gt and produces a low-level atomic action at ∼µlo(st, gt), which is applied\nto the environment. The environment then yields a reward Rt sampled from an unknown reward\nfunction R(st, at) and transitions to a new state st+1 sampled from an unknown transition function\nf(st, at). The higher-level controller provides the lower-level with an intrinsic reward rt = r(st, gt, at, st+1),\nusing a fixed parameterized reward function r. The lower-level policy will store the experience (st, gt, at, rt, st+1, h(st, gt, st+1)) for off-policy training.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
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| "text": "The higher-level policy collects the environment rewards Rt and, every c time steps, stores the higher-level transition\n(st:t+c−1, gt:t+c−1, at:t+c−1, Rt:t+c−1, st+c) for off-policy training. 3.2 Parameterized Rewards Our higher-level policy produces goals gt indicating desired relative changes in state observations. That is, at step t, the higher-level policy produces a goal gt, indicating its desire for the lower-level\nagent to take actions that yield it an observation st+c that is close to st + gt. Although some state\ndimensions (e.g., the position of the quadrupedal robot in Figure 3) are more natural as goal subspaces,\nwe chose this more generic goal representation to make it broadly applicable, without any manual\ndesign of goal spaces, primitives, or controllable dimensions. This makes our method general and easy to apply to new problem settings. To maintain the same absolute position of the goal regardless\nof state change, the goal transition model h is defined as h(st, gt, st+1) = st + gt −st+1. (2) We define the intrinsic reward as a parameterized reward function based on the distance between the\ncurrent observation and the goal observation: r(st, gt, at, st+1) = −||st + gt −st+1||2. (3)", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
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| "text": "This rewards the lower-level policy for taking actions that yield observations that are close to\nthe desired value st + gt. In our evaluations on simulated ant locomotion, we use all positional\nobservations as the representation for gt, without distinguishing between the (x, y, z) root position\nor the joints, making for a generic and broadly applicable choice of goal space. The reward r and\ntransition function h are computed only with respect to these positional observations.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
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| "text": "See Figure 3\nfor an example of the goals gt chosen during a successful navigation of a complex environment. The lower-level policy may be trained using standard methods by simply incorporating gt as an\nadditional input into the value and policy models. For example, in DDPG, the equivalent objective to\nEquation 1 in terms of lower-level Q-value function Qloθ is to minimize the error\n(Qloθ (st, gt, at) −r(st, gt, at, st+1) −γQloθ (st+1, gt+1, µloφ (st+1, gt+1)))2, (4) for all transitions (st, gt, at, st+1, gt+1). The policy µloφ would be trained to maximize the Q-value\nQloθ (st, gt, µloφ (st, gt)) for all sampled state-goal tuples (st, gt). Parameterized rewards are not a new concept, and have been studied previously [38, 20]. They are a\nnatural choice for a generally applicable HRL method and have therefore appeared as components\nof other HRL methods [48, 24, 33, 26]. A significant distinction between our method and these\nprior approaches is that we directly use the state observation as the goal, and changes in the state\nobservation as the action space for the higher-level policy, in contrast to prior methods that must\ntrain the goal representation. This allows the lower-level policy to begin receiving reward signals\nimmediately, even before the lower-level policy has figured out how to reach the goal and before the\ntask's extrinsic reward provides any meaningful supervision. In our experiments (Section 5), we find\nthat this produces substantially better results.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
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| "text": "3.3 Off-Policy Corrections for Higher-Level Training While a number of prior works have proposed two-level HRL architectures that involve some sort of\ngoal setting, such designs in previous work generally require on-policy training [48]. This is because\nthe changing behavior of the lower-level policy creates a non-stationary problem for the higher-level\npolicy, and old off-policy experience may exhibit different transitions conditioned on the same goals. However, for HRL methods to be applicable to real-world settings, they must be sample-efficient,\nand off-policy algorithms (often based on some variant of Q-function learning) generally exhibit\nsubstantially better sample efficiency than on-policy actor-critic or policy gradient variants. In this\nsection, we describe how we address the challenge of off-policy training of the higher-level policy. We would like to take the higher-level transition tuples (st:t+c−1, gt:t+c−1, at:t+c−1, Rt:t+c−1, st+c),\nwhere xt:t+c−1 denotes the sequence xt, . . . , xt+c−1, which are collected by the higher-level policy\nand convert them to state-action-reward transitions (st, gt, P Rt:t+c−1, st+c) that can be pushed\ninto the replay buffer of any standard off-policy RL algorithm. However, since transitions obtained\nfrom past lower-level controllers do not accurately reflect the actions (and therefore resultant states\nst+1:t+c) that would occur if the same goal were used with the current lower-level controller, we must\nintroduce a correction that translates old transitions into ones that agree with the current lower-level\ncontroller. Our main observation is that the goal gt of a past high-level transition (st, gt, P Rt:t+c−1, st+c) may\nbe changed to make the actual observed action sequence more likely to have happened with respect\nto the current instantiation of µlo. The high-level action gt which in the past induced a low-level\nbehavior at:t+c−1 ∼µlo(st:t+c−1, gt:t+c−1) may be re-labeled to a goal ˜gt which is likely to induce\nthe same low-level behavior with the current instantiation of the lower-level policy. Thus, we propose\nto remedy the off-policy issue by re-labeling the high-level transition (st, gt, P Rt:t+c−1, st+c) with\na different high-level action ˜gt chosen to maximize the probability µlo(at:t+c−1|st:t+c−1, ˜gt:t+c−1), where the intermediate goals ˜gt+1:t+c−1 are computed using the fixed goal transition function h. In\neffect, each time we modify the low-level policy µlo, we would like to answer the question: for which\ngoals would this new controller have taken the same actions as the old one? Most RL algorithms will use random action-space exploration to select actions, which means that\nthe behavior policy (even for deterministic algorithms such as DDPG [27]) is stochastic and the log\nprobability log µlo(at:t+c−1|st:t+c−1, ˜gt:t+c−1) may be computed as t+c−1\nlog µlo(at:t+c−1|st:t+c−1, ˜gt:t+c−1) ∝−1 X ||ai −µlo(si, ˜gi)||22 + const. (5)\ni=t", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "To approximately maximize this quantity in practice, we compute this log probability for a number of\ngoals ˜gt, and choose the maximal goal to re-label the experience. In our implementation, we calculate\nthe quantity on eight candidate goals sampled randomly from a Gaussian centered at st+c −st. We\nalso include the original goal gt and a goal corresponding to the difference st+c −st in the candidate\nset, to have a total of 10 candidates. This provides a suitably diverse set of ˜gt to approximately\nsolve the arg max of Equation 5, while also biasing the result to be closer to candidates ˜gt which\nwe believe to be appropriate given our knowledge of the problem (see additional implementation\ndetails in the Appendix). Our approach here is only an approximation, and we elaborate on possible\nalternative off-policy corrections in the Appendix.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "Discovering meaningful and effective hierarchies of policies is a long standing research problem\nin RL [7, 32, 43, 8, 2]. Classically, the work on HRL focused on discrete state domains, where\nstate visitation and transition statistics can be used to construct heuristic sub-goals for low-level\npolicies [41, 29, 5]. The options framework [43, 35], a popular formulation for HRL, proposes a\ntermination policy for each sub-policy (option). While the traditional options framework relies on\nprior knowledge for designing options, [2] recently derived an actor-critic algorithm for learning\nthem jointly with the higher-level policy. This option-critic architecture [2] is an important step\ntoward end-to-end HRL; however, such approaches are often prone to learning either a sub-policy that\nterminates every time step, or one effective sub-policy that runs through the whole episode. In practice,\nregularizers are essential to learn multiple effective and temporally abstracted sub-policies [2, 17, 47]. To guarantee learning useful sub-policies, recent work has studied approaches that provide auxiliary\nrewards for the low-level policies [5, 19, 24, 44, 10]. These approaches rely on hand-crafted rewards\nbased on prior domain knowledge [23, 19, 24, 44] or diversity-encouraging rewards like mutual\ninformation [6, 10]. A number of works have suggested that semantically distinct behavior can be\ninduced by training on a set of diverse tasks, and have suggested pre-training the lower-level policy\non such tasks [19, 10], or training the multi-level hierarchical policy in a multi-task setup [11, 40]. However, having access to a collection of suitably similar tasks is a luxury which is not always\navailable and may require hand-design. Our method uses a generic reward that is specified with\nrespect to the state space, and therefore avoids designing various rewards or multiple tasks. Another difference from most HRL work [10, 11] is that we use off-policy learning, leading to\nsignificant improvements in sample efficiency. In end-to-end HRL, off-policy RL creates a nonstationary problem for the higher-level policy, since the lower-level is constantly changing. We are\naware of only one recent work which applies HRL in an off-policy setting [26].", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "As in our work, the\nauthors devise a hierarchical structure in which a lower-level policy is trained to reach observations\ndirected by a higher-level policy. The multiple layers of policies are trained jointly in an off-policy\nmanner, while ignoring the non-stationarity problem which we realize is a key issue for off-policy\nHRL. Accordingly, we derive and test an off-policy correction in the context of HRL, and empirically\nshow that this technique is crucial to successfully train hierarchical policies on complex tasks. Our work is related to FeUdal Networks (FuN) [48], originally inspired from feudal RL [7]. FuN\nalso makes use of goals and a parameterized lower-level reward. Unlike our method, FuN represents\nthe goals and computes the rewards in terms of a learned state representation. In our experiments,\nwe found this technique to under-perform compared to our approach, which uses the state in its raw\nform. We find that this has a number of benefits. For one, the lower-level policies can immediately\nbegin receiving intrinsic rewards for reaching goals even before the higher-level policy receives a\nmeaningful supervision signal from the task reward. Additionally, the representation is generic and Ant Gather Ant Maze Ant Push Ant Fall\nHIRO 3.02±1.49 0.99±0.01 0.92±0.04 0.66±0.07\nFuN representation 0.03 ± 0.01 0.0 ± 0.0 0.0 ± 0.0 0.0 ± 0.0\nFuN transition PG 0.41 ± 0.06 0.0 ± 0.0 0.56 ± 0.39 0.01 ± 0.02\nFuN cos similarity 0.85 ± 1.17 0.16 ± 0.33 0.06 ± 0.17 0.07 ± 0.22\nFuN 0.01 ± 0.01 0.0 ± 0.0 0.0 ± 0.0 0.0 ± 0.0\nSNN4HRL 1.92 ± 0.52 0.0 ± 0.0 0.02 ± 0.01 0.0 ± 0.0\nVIME 1.42 ± 0.90 0.0 ± 0.0 0.02 ± 0.02 0.0 ± 0.0 Table 1: Performance of the best policy obtained in 10M steps of training, averaged over 10 randomly\nseeded trials with standard error. Comparisons are to variants of FuN [48], SNN4HRL [10], and\nVIME [21]. Even after extensive hyper-parameter searches, we were unable to achieve competitive\nperformance from the baselines on any of our tasks. In the Appendix, we include the only competitive\nresult we could achieve – VIME on Ant Gather trained for a much longer amount of time.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "Goal-conditioned value functions [28, 42, 38, 1, 34] are actively explored outside\nthe context of HRL. Continued progress in this field may be used to further improve HRL methods. In our experiments, we compare HIRO method to prior techniques, and ablate the various components\nto understand their importance. Our experiments are conducted on a set of challenging environments that require a combination of locomotion and object manipulation. Visualizations of these\nenvironments are shown in Figure 1. See the Appendix for more details on each environment.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "The ant gather task is a standard task introduced in [9]. A simulated ant must navigate to\ngather apples while avoiding bombs, which are randomly placed in the environment at the beginning\nof each episode. The ant receives a reward of 1 for each apple and a reward of −1 for each bomb.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "For the first difficult navigation task we adapted the maze environment introduced in [9]. In this environment an ant must navigate to various locations in a '⊃'-shaped corridor. We increase\nthe default size of the maze so that the corridor is of width 8. In our evaluation, we assess the success\nrate of the policy when attempting to reach the end of the maze. In this task we introduce a movable block which the agent can interact with. A greedy\nagent would move forward, unknowingly pushing the movable block until it blocks its path to the\ntarget. To successfully reach the target, the ant must first move to the left around the block and then\npush the block right, clearing the path towards the target location. This task extends the navigation to three dimensions.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "The ant is placed on a raised platform,\nwith the target location directly in front of it but separated by a chasm which it cannot traverse by\nitself. Luckily, a movable block is provided on its right. To successfully reach the target, the ant must\nfirst walk to the right, push the block into the chasm, and then safely cross.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "5.1 Comparative Analysis The primary comparisons to previous HRL methods are done with respect to FeUdal Networks\n(FuN) [48], stochastic neural networks for HRL (SNN4HRL) [10], and VIME [21] (see Table 1, and\nAppendix for more details). As these algorithms often come with problem-specific design choices,\nwe modify each for fairer comparisons. In terms of problem assumptions, our work is closest to\nthat of FuN which is applicable to any single task without specific sub-policy reward engineering. MLSH [11] is another promising recent work for HRL; however, since it relies on learning meaningful\nsub-policies through experiencing multiple, diverse, hand-designed tasks, we do not include explicit\ncomparisons. We leave exploring our method in the context of multi-task learning for future work. FeUdal Network (FuN). Unlike SNN4HRL or VIME, the official open-source code for FuN was not\navailable at the time of submission, and therefore we aimed to replicate key design choices of FuN\nfrom our algorithm implementation. FuN [48] primarily proposes four components: (1) transition\npolicy gradient, (2) directional cosine similarity rewards, (3) goals specified with respect to a learned\nrepresentation, and (4) dilated RNN. Since our tasks are low-dimensional and fully observed, we do Ant Gather Ant Maze Ant Push Ant Fall", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "2.0 0.4\n0.6 0.3\n1.5 0.3\n0.4 0.2\n1.0 0.2 0.0 0.0 0.0 0.0\n0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 HIRO With pre-training No HRL\nWith lower-level re-labelling No off-policy correction Figure 4: Results of our method and a number of variants on a set of difficult tasks. Each plot\nshows average reward (for Ant Gather) or average success rate (for the rest; see Appendix) over 10\nrandomly seeded trials, with x-axis in millions of environment steps. We find that HIRO can perform\nwell across all tasks. We also note that HIRO learns rapidly; on the complex navigation tasks it\nrequires only a few million environment steps (a few days in real-world interaction time) to achieve\ngood performance. Our method is only out-performed on Ant Gather by a variant that pre-trains the\nlower-level policy (thus not needing an off-policy correction). not include design choice (4). For each of (1), (2), and (3), we apply an equivalent modification of\nour HRL method and evaluate its performance on the same tasks. We also evaluate all modifications\ntogether as an approximation to the entire FuN paradigm.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "Results in Table 1 show that on our tasks,\nthe FuN modifications do not learn well, and other than Ant Gather are significantly out-performed by\nHIRO. In particular, it is worth noting that the use of learned representations, rather than observation\ngoals, leads to almost no improvement on the tasks. This suggests that the choice of using goal\nobservations as lower-level goals significantly improves HRL performance, by providing a strong\nsupervision signal to the lower-level policy right from the beginning of training. Stochastic Neural Networks for HRL (SNN4HRL). SNN4HRL [10] initially trains the low-level\npolicy with a proxy reward to encourage learning useful diverse exploration policies, and then the\nhigh-level policy is trained in the tasks of interest while the low-level is fixed. While SNN4HRL can\nperform better than FuN, it is still far behind our proposed HRL method.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "Variational Information Maximizing Exploration (VIME). VIME [21] is not an HRL method but\nis used as a strong baseline in SNN4HRL. As discussed in [10] and matched by our results, for the\nbenchmark's short horizon task of length 500, it performs approximately the same as SNN4HRL. Option-Critic Architecture. We extended the option-critic architecture implementation [2] for\ncontinuous actions and attempted a number of alternative variants besides the naïve modification\nof the original. No versions yielded reasonable performance in our tasks, and so we omit it from\nthe results. This is possibly due to difficulty in continuous control tasks, but most importantly the\noption-critic sub-policies rely solely on the external reward, making learning gait policies difficult.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
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| "text": "5.2 Ablative Analysis In Figure 4 we present results of our proposed HRL method (\"HIRO\") compared with a number of\nvariants to understand the importance of various design choices: With lower-level re-labelling. We evaluate the benefit of recent proposals [1, 25] to increase the\namount of data available to an agent trained using a parameterized reward (the lower-level policy\nin our setup) by re-labeling experiences with randomly sampled goals. This allows the lower-level\npolicy to use experience collected with respect to a specific goal g to be used to learn behavior with\nrespect to any alternative goal ˜g. Our results show that this technique can provide an initial speed-up\nin training; however, its performance is quick to plateau. We hypothesize that re-labeling goals\nrandomly may make lower-level training more difficult, since the policy must learn to not only satisfy\nthe goals provided by the higher-level agent, but instead almost any conceivable goal. The benefit of\nre-labeling goals will require more research, and we encourage future work to investigate better ways\nto harness its benefits. In this variant we evaluate a simpler method to avoid the non-stationary issue\nin higher-level off-policy training. Rather than correct for past experiences, we instead pre-train\nthe lower-level policy for 2M steps (using goals sampled from a Gaussian) before freezing it and\ntraining the higher-level policy alone (this variant also has the advantage of allowing the higher-level\npolicy to learn with respect to a deterministic, non-exploratory lower-level policy). In the harder\nnavigation tasks, we find that pre-training is detrimental. This is understandable, as these tasks require\nspecialization in different low-level behavior for different stages of the navigation. By allowing the\nlower-level policy to continually learn as new parts of the environment are encountered, we are able\nto learn a lower-level policy which is better able to satisfy the desired goals of the higher-level. In\ncontrast, in the simpler and mostly homogeneous Ant Gather task, the advantage of pre-training is\nsignificant. This suggests that our off-policy correction is still not perfect, and there is potentially\nsignificant benefit to be obtained by improving it.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "No off-policy correction. We assess the advantage of including the off-policy correction compared\nto training off-policy naïvely, ignoring the non-stationary issue. Interestingly, training an HRL policy\nthis way can do quite well. However, in the harder tasks (Ant Push, Ant Fall) the issue becomes\ndifficult to ignore.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "Accordingly, we observe a significant benefit from using the off-policy correction. Finally, we evaluate the ability of a single non-HRL policy to learn in these environments. This variant makes almost no progress on the tasks compared to our HRL method.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
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| "text": "We have presented a method for training a two-layer hierarchical policy. Our approach is general,\nusing learned goals to pass instructions from the higher-level policy to the lower-level one. Moreover,\nwe have described a method by which both polices may be trained in an off-policy manner concurrently\nfor highly sample-efficient learning. Our experiments show that our method outperforms prior HRL\nalgorithms and can solve exceedingly complex tasks that combine locomotion and rudimentary object\ninteraction. We note that our results are still far from perfect, and there is much work left for future\nresearch to improve the stability and performance of HRL methods on these tasks. We thank Ben Eysenbach and others on the Google Brain team for insightful comments and discussions. [1] Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder,\nBob McGrew, Josh Tobin, OpenAI Pieter Abbeel, and Wojciech Zaremba. Hindsight experience\nreplay. In Advances in Neural Information Processing Systems, pages 5048–5058, 2017. [2] Pierre-Luc Bacon, Jean Harb, and Doina Precup. The option-critic architecture. In AAAI, pages\n1726–1734, 2017. [3] Gabriel Barth-Maron, Matthew W Hoffman, David Budden, Will Dabney, Dan Horgan, Alistair\nMuldal, Nicolas Heess, and Timothy Lillicrap. Distributed distributional deterministic policy [4] Andrew G Barto and Sridhar Mahadevan.", |
| "paper_id": "1805.08296", |
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| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
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| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
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| "text": "Sample efficient actor-critic with experience replay. International\nConference on Learning Representations, 2017. A Discussion on Alternative Off-Policy Corrections for High-Level Actions Through our experiments, we found that our proposed maximum likelihood-based action relabeling\nworks well empirically; however, we also tried other variants of off-policy correction schemes. While none of the methods below worked as well as ours in the tested domains based on preliminary\nexperiments, we summarize them below as a reference for further future work on off-policy correction\nfor HRL. The experience replay stores (st:t+c, at:t+c−1, gt:t+c−1, Rt:t+c−1, st+c) sampled from following a\nlow-level policy ai ∼µloβ (ai|si, gi). ai is low-level action and gi is high-level action (or goal for\nthe low-level policy). We want to estimate the following objective for the current low-level policy\nµlo(a|s, g), where Qhi represents the target network, h 2i L(θ) = Eβ Qhiθ (st, gt) −yt (6) yt = EQt+c−1i=t µlo(ai|si,gi)p(si+1|st,ai) Rt:t+c−1 + γ maxg Qhi(st+c, g) (7) = EQt+c−1i=t µloβ (ai|si,gi)p(si+1|st,ai) wt · Rt:t+c−1 + γ maxg Qhi(st+c, g) (8)\nt+c−1 µlo(ai|si, gi)\nwt = Y (9) µloβ (ai|si, gi). i=t We remind the reader that gi is computed using a deterministic dynamics from gt using gi+1 =\nh(st, gt, st+1) = si + gi −si+1 for i = t, t + 1, . . . , t + c −2. Direct Importance Correction. A naïve approach is to directly use the unbiased estimator based on\nimportance weighting defined by the expectation in Eq. 9,", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "h 2i L(θ) = Eβ Qhiθ (st, gt) −ˆyt (10) ˆyt = wt Rt:t+c−1 + γ max Qhi(st+c, g) (11)\nt+c−1 µlo(ai|si, gi)\nwt = Y (12) µloβ (ai|si, gi). i=t For the continuous action domains in our paper, we found this estimator, while unbiased, has very\nhigh variance, and does not work well in practice. Importance-Based Action Relabeling. Instead of computing the high-variance importance weight\nfor the sample goal gt, we may also try to find a new goal ˜gt such that the importance weight is\napproximately 1. This leads to the action relabeling objective as used in our method, h 2i L(θ) = Eβ Qhiθ (st, ˜gt) −ˆyt (13)\nˆyt = Rt:t+c−1 + γ max Qhi(st+c, g), (14) where ˜gt can be found by minimizing loss functions such as,\nt+c−1 !2 µlo(ai|si, gi)\n˜gt = arg min 1 − Y (15)\ngt µloβ (ai|si, gi) i=t\nt+c−1 !2\n˜gt = arg min X log µlo(ai|si, gi) −log µloβ (ai|si, gi) . (16)\ni=t\nSince there is no guarantee that ˜gt exists to make the loss function go to 0, this estimator is still biased. However, we could expect that the bias may be reduced.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "Model-Based Relabeling. What we need to ensure for off-policy correction is that\n(st:t+c−1, gt:t+c−1, st+c) is consistent with the dynamics of MDP transition p(si+1|si, ai) and current low-level policy µlo(ai|si, gi). If we can approximate either the high-level forward dynamics\n˜st+c = phi(·|st, gt) or the inverse model ˜gt ∼phiinv(·|st, si+c), then we may directly do model-based\nprediction to relabel for either st+c or gt. While the action relabeling TD objective is given as Eq. 14,\nthe state relabeling objective is given by,\nh 2i L(θ) = Eβ Qhiθ (st, gt) −ˆyt (17)\nˆyt = Rt:t+c−1 + γ max Qhi(˜st+c, g). (18)\nThe question is how to get phi or phiinv.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "While we can fit parametric functions on samples of data, this\nis often as difficult as fully model-based approach. We may instead make use of that fact that the\nlow-level is trying to reach the given goal states. Assuming the low-level policy eventually gets to\ncomplete the given goals, we may use the following forms,\nphi(˜st+c|st, gt) = N(st + gt, Σ) (19)\nphiinv(˜gt|st, st+c) = N(st+1 −st, Σ). (20)\nThis resembles transition policy gradient in FuN [48], where the high-level policy is trained by\nassuming the low-level approximately completes the assigned goals. Empirically, we did not observe\nthis outperformed our approach on the tested domains.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "B Environment Details Environments use the MuJoCo simulator [45] with dt = 0.02 and frame skip set to 5. We use the Gather environment provided by Rllab with a simulated ant agent. The ant is equivalent\nto the standard Rllab Ant, except that its gear range is reduced from (−150, 150) to (−30, 30). In\naddition to observing qpos, qvel, and the current time step t, the agent also observes depth readings\nas defined by the standard Gather environment. We set the activity range to 10 and the sensor span to\n2π, which matches the settings in [10]. Each episode is terminated either when the ant falls or at 500 steps. The reward used is the default reward (number of apples minus number of bombs). We devise three navigation tasks to evaluate our method. In each navigation task, we create an\nenvironment of 8 × 8 × 8 blocks, some movable and some with fixed position.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "We use the same ant\nagent used in Gather. The agent observes qpos, qvel, the current time step t, and the target location. Its actions correspond to torques applied to joints. At the beginning of each episode, the environment\nsamples a target position (gx, gy) and the agent is provided a reward at each step corresponding\nto negative L2 distance from the target: −p(gx −x)2 + (gy −y)2. In one of the navigation tasks\n(Falling), the L2 distance is measured with respect to 3 coordinates: x, y, and z. Each episode is 500\nsteps long (i.e., the episode does not terminate when the ant falls).", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "We describe the specifics of each navigation task below. In this task, immovable blocks are placed to confine the agent to a \"⊃\"-shaped corridor. That is,\nblocks are placed everywhere except at (0, 0), (8, 0), (16, 0), (16, 8), (16, 16), (8, 16), (0, 16). The\nagent is initialized at position (0, 0). At each episode, a target position is sampled uniformly at\nrandom from gx ∼[−4, 20], gy ∼[−4, 20]. At evaluation time, we evaluate the agent only on its ability to reach (0, 16). We define a \"success\"\nas being within an L2 distance of 5 from the target on the ultimate step of the episode.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "In this task, immovable blocks are placed everywhere except at\n(0, 0), (−8, 0), (−8, 8), (0, 8), (8, 8), (16, 8), (0, 16). A movable block is placed at (0, 8). The agent\nis initialized at position (0, 0). At each episode, the target position is fixed to (gx, gy) = (0, 19).", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "Therefore, the agent must first move to the left, the push the movable block to the right, and then\nnavigate to the target unimpeded. At evaluation time, we evaluate the agent on its ability to reach (0, 19). We define a \"success\" as\nbeing within an L2 distance of 5 from the target on the ultimate step of the episode. In this task, the agent is initialized on a platform of height 4.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "Immovable blocks are placed everywhere\nexcept at (−8, 0), (0, 0), (−8, 8), (0, 8), (−8, 16), (0, 16), (−8, 24), (0, 24). The raised platform is\nabsent in the region [−4, 12] × [12, 20]. A movable block is placed at (8, 8). The agent is initialized\nat position (0, 0, 4.5). At each episode, the target position is fixed to (gx, gy, gz) = (0, 27, 4.5).", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "Therefore, to cross the chasm, the agent must first push the movable block into the chasm and walk\non top of it before navigating to the target. At evaluation time, we evaluate the agent on its ability to reach (0, 27, 4.5). We define a \"success\" as\nbeing within an L2 distance of 5 from the target on the ultimate step of the episode.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "C Implementation Details C.1 Network Structure We use the same basic network structure as proposed by the TD3 algorithm [12], with the only\ndifference being that we use layers of size (300, 300) rather than (400, 300). The output of the lower-level actor network (activated by tanh) is scaled to the range of the low-level\nactions, which is ±30. The output of the higher-level actor network is scaled to an approximated range of high-level actions:\n±10 for the desired relative x, y; ±0.5 for the desired relative z; ±1 for the desired relative torso\norientations; and the remaining limb angle ranges are available from the ant.xml file. C.2 Training Parameters • Discount γ = 0.99 for both controllers.\n• Adam optimizer; actor learning rate 0.0001; critic learning rate 0.001.\n• Soft update targets τ = 0.005 for both controllers.\n• Replay buffer of size 200,000 for both controllers.\n• Lower-level train step and target update performed every 1 environment step.\n• Higher-level train step and target update performed every 10 environment steps.\n• No gradient clipping.\n• Reward scaling of 1.0 for lower-level; 0.1 for higher-level.\n• Lower-level exploration is Gaussian noise with σ = 1.0.\n• Higher-level exploration is Gaussian noise with σ = 1.0. Figure 5: Performance of HIRO compared to VIME and SNN4HRL, averaged over 10 trials with xaxis in millions of experience samples. After a hyper-parameter search on the baselines, we were only\nable to get competitive performance with HIRO from VIME on Ant Gather, with a significantly higher\namount of experience. On the other tasks, we were unable to achieve good baseline performance, even\nwith more experience. The SNN4HRL curve does not include 25M transitions used in pre-training.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "C.3 Off-Policy Correction Given a high-level experience transition (st:t+c−1, gt:t+c−1, at:t+c−1, Rt:t+c−1, st+c), we select 10\ncandidate ˜gt to maximize the log-probability of the lower-level actions. One is taken to be the original\ngt; another to be st+c −st; and the remaining eight are sampled randomly from a Gaussian centered\nat st+c −st with standard deviation 0.5 × 12[high-level action range] (and subsequently clipped to\nlie within the high-level action range). Learned hierarchical policies are evaluated every 50,000 training steps by averaging performance\nover 50 random episodes. FuN [48] primarily proposes four components: (1) transition policy gradient, (2) directional cosine\nsimilarity rewards, (3) goals specified with respect to a learned representation, and (4) dilated RNN. Since our tasks are low-dimensional and fully observed, we do not include design choice (4).", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "For\neach of (1), (2), and (3), we apply an equivalent modification of our HRL method and evaluate\nits performance on the same tasks. For representation learning, we augment our method with a\ntwo-hidden-layer feed-forward neural network for embedding the observations before passing them to\nthe lower and higher-level policies. The higher-level policy specifies high-level actions and rewards\nlow-level behavior with respect to this representation. For the transition policy gradient, we modify\nour off-policy correction to instead replace a goal gt with a goal ˜gt sampled from a Gaussian centered\nat st+c −st, with standard deviation set to 0.1 × 12[high-level action range]. This is analogous to\nFuN's transition policy gradient, which trains the higher-level policy under the assumption that its\nstate transitions are distributed symmetrically around its proposed goals. For directional rewards, we\nreplace our relative position parameterized reward function r with a cosine similarity reward function\nequivalent to that used in FuN. SNN4HRL [10] trains the hierarchical policy stage-wise. It first uses a proxy reward with mutual\ninformation (MI) bonus to learn a mixture of low-level skills encouraging diverse movements, and\nthen trains a high-level policy that controls switching among these skills to optimize for the task\nreward. We imported our additional environments to the official open-source codes with minimal\nmodifications and followed the similar benchmark setup as in [10]. All policies are trained with Figure 6: Visitation plots for 2 random seeds for the low-level SNN policy in the SNN4HRL\nbenchmark. All 6 policies diversify in different exploration directions. TRPO [39] with step size 0.01 and discount 0.99.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "All neural networks (the SNN, the Latent Regressor\nNetwork and the Manager Network) have 2 layers of 32 hidden units as done in [10]3. We report the\nfinal results averaged over 10 random seeds, where we ran the low-level training using 5 seeds, and\nran the high-level training using 2 seeds per trained low-level policy. For the skill training, the mesh density used to grid the (x, y) space and give the MI bonus is 10\ndivisions/unit, and the mutual information bonus coefficient αH is set to 10. Bilinear integration is\nused for the SNN. The number of skills trained is 6. The batch size and the maximum path length for\nthe pre-train task are 50,000 and 500 respectively. To guarantee learning effective skills, we trained\nthe policy with 500 updates, or 25M transitions. The visualization of learned skill primitives is shown\nin Figure 6, where the learned 6 sub-policies successfully cover different exploration directions. For the high-level policy learning4, we fixed the low-level policies as done in SNN4HRL and trained\na policy that outputs a categorical action every 10 time steps that choose which skill to execute. For\nfair comparisons, we experimented with both sparse and dense rewards for the maze environments,\nand searched over batch sizes for (1e4, 5e4, 5e5) transitions. We observed that the dense rewards did\nnot help for SNN4HRL significantly, since the policy often quickly converge to local optimum. We\nfound the batch size of 1e4 is too noisy, and the batch size of 5e5 is unnecessarily sample intensive,\nso the high-level policy is trained using batch size of 5e4, the default value in their paper, for 300\nupdates, or 15M transitions. The combined training sample size of 40M is generously more than 10M\nused for our methods; however, our method still outperforms these SNN4HRL results substantially. D.3 Variational Information Maximizing Exploration Variational Information Maximizing Exploration (VIME) [21], while not a HRL algorithm, exhibits\ngood performance on prior benchmark maze and gather tasks, and is also used as a strong baseline\nin SNN4HRL [10].", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "We ran the algorithm using the default settings in the official open-source\nimplementation. Batch size of 50,000 is used. We report the average performance across 5 seeds\nafter running the algorithm for 300 updates, or 15M transitions. Only the Gather task required\nmore samples to converge to the final performance, and required 25M+ transitions to reach the same\nperformance as what our method reached in a few million transitions. 3While the policy network sizes are significantly smaller than those used for our method, we observed no\nsignificant improvements with larger network sizes and this observation conforms with prior results that on-policy\npolicy gradient methods can perform well on MuJoCo benchmark tasks with very small networks [9, 37].\n4In both SNN4HRL [10] and VIME [21], primarily the results are reported and compared on SwimmerMaze\nand SwimmerGather, and therefore the experimental results are different. D.4 Option-Critic Architecture We also experimented with continuous-action variants of the option-critic architecture [2]. The\noption-policy πω,θ(a|s) for option ω is parameterized as a Gaussian, whose mean is output from\na neural network taking in s and ω, and variance is chosen to be global and diagonal. We first\ntested naively extending the official open-source implementation for continuous action, and then tried\nmodifying the learning procedure such that the critic learns the state-option-action value function\nQU(s, ω, a) instead of the state-option value function QΩ(s, ω) in the original implementation. This\ncreates slight changes for the value and policy training objectives, while the loss for termination\npolicy βω,ν(s) is basically kept the same. Concretely, for the first variant, we trained QΩ(s, ω) and\nthe option-policy πω,θ(a|s) with the following gradients, gΩ= Est,ωt,st+1∼β ∂Ω(QΩ(st, ωt) −yt)2 (21)\ngθ = Est,ωt,at,st+1∼π [(yt −bt) ∇θ log πωt,θ(at|st)] (22)\nyt = rt+1 + γ (1 −βωt,ν(st+1)) Q′(st+1, ωt) + βωt,ν(st+1) max Q′(st+1, ω) (23) where Q′ represents the target network, and β and π represent using off-policy and on-policy transition\nsamples respectively. For simplicity of explanation, we assumed that the reward only depends on\nstates, but similar arguments can be made for the general case. There are two pragmatic problems\nfor this objective.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "First, the policy gradient, which relies on a score function estimate, could be high\nvariance especially with respect to a continuous policy πω,θ. We experimented with several choices of\nbaselines bt, including QΩ(st, ωt) and Q; (st, ωt). The second problem is that the off-policy learning\nfor QΩ(st, ωt) does not use the action at taken and only relies on ωt. This effectively creates the\nsame non-stationarity problem with respect to the high-level policy as our method, since it ignores\nthat for the same ωt and st, the next state st+1 can be different due to changing πω,θ. To counter\nboth problems, we also explored another variant of the option-critic implementation at the expense of\npotentially more computation and network parameters, which conforms more closely with the policy\ngradient theorems in the original paper. Specifically, we trained QU(s, ω, a) and the option-policy\nπω,θ(a|s) with the following gradients, gU = Est,ωt,at,st+1∼β (QU(st, ωt, at) −yt)2 (24)\nh i gθ = Est,ωt∼π ∇θEa∼πωt,θ(a|st) [QU(st, ωt, a)] (25) yt = rt+1 + γ (1 −βωt,ν(st+1)) Q′(st+1, ωt) + βωt,ν(st+1) max Q′(st+1, ω) (26)\nQ′(s, ω) = Ea∼πω,θ(a|s) [Q′(s, ω, a)] . (27) In this implementation, we observe that the off-policy learning for QU(s, ω, a) can effectively utilize\nboth ωt and at, removing the non-stationarity problem, and the policy gradient can be estimated with\nlower variance using reparametrization trick [22] through the critic directly. Furthermore, since the\npolicy gradient no longer requires next state estimate, off-policy state samples may also be used along\nwith enumeration over all ω,", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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| "text": "# \"X . (28) gθ = Est∼β ∇θEa∼πω,θ(a|st) [QU(st, ω, a)] Making similar approximations for the termination policy, this enables a fully off-policy actor-critic\nalgorithm like DDPG [27] for the option-critic architecture. While we tried these modifications, we could not make the option-critic implementation work\nreasonably on our domains. The main difficulty is likely because the low-level option-policies are\nlearned using only the external task reward, a limitation in a direct end-to-end hierarchical policy\nstructure. While in our experiments we could not show substantial successes, the algorithm may work\nbetter with more sophisticated modifications to the policy evaluation or policy improvement routines\nbased on recent advances [30, 49, 14, 16, 12], and we leave further comparisons for future work.", |
| "paper_id": "1805.08296", |
| "title": "Data-Efficient Hierarchical Reinforcement Learning", |
| "authors": [ |
| "Ofir Nachum", |
| "Shixiang Gu", |
| "Honglak Lee", |
| "Sergey Levine" |
| ], |
| "published_date": "2018-05-21", |
| "primary_category": "cs.LG", |
| "arxiv_url": "http://arxiv.org/abs/1805.08296v4", |
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