We propose a novel hybrid stochastic policy gradient estimator by combining an unbiased policy gradient estimator, the REINFORCE estimator, with another biased one, an adapted SARAH estimator for policy optimization. The hybrid policy gradient estimator is shown to be biased, but has variance reduced property. Using this estimator, we develop a new Proximal Hybrid Stochastic Policy Gradient Algorithm (ProxHSPGA) to solve a composite policy optimization problem that allows us to handle constraints or regularizers on the policy parameters. We first propose a single-looped algorithm then introduce a more practical restarting variant. We prove that both algorithms can achieve the best-known trajectory complexity $\mathcal{O}\left(\varepsilon^{-3}\right)$ to attain a first-order stationary point for the composite problem which is better than existing REINFORCE/GPOMDP $\mathcal{O}\left(\varepsilon^{-4}\right)$ and SVRPG $\mathcal{O}\left(\varepsilon^{-10/3}\right)$ in the non-composite setting. We evaluate the performance of our algorithm on several well-known examples in reinforcement learning. Numerical results show that our algorithm outperforms two existing methods on these examples. Moreover, the composite settings indeed have some advantages compared to the non-composite ones on certain problems.
Traditional policy gradient methods are fundamentally flawed. Natural gradients converge quicker and better, forming the foundation of contemporary Reinforcement Learning such as Trust Region Policy Optimization (TRPO) and Proximal Policy Optimization (PPO). This lecture note aims to clarify the intuition behind natural policy gradients, focusing on the thought process and the key mathematical constructs.
We study policy optimization for Markov decision processes (MDPs) with multiple reward value functions, which are to be jointly optimized according to given criteria such as proportional fairness (smooth concave scalarization), hard constraints (constrained MDP), and max-min trade-off. We propose an Anchor-changing Regularized Natural Policy Gradient (ARNPG) framework, which can systematically incorporate ideas from well-performing first-order methods into the design of policy optimization algorithms for multi-objective MDP problems. Theoretically, the designed algorithms based on the ARNPG fr…
Policy-gradient approaches to reinforcement learning have two common and undesirable overhead procedures, namely warm-start training and sample variance reduction. In this paper, we describe a reinforcement learning method based on a softmax value function that requires neither of these procedures. Our method combines the advantages of policy-gradient methods with the efficiency and simplicity of maximum-likelihood approaches. We apply this new cold-start reinforcement learning method in training sequence generation models for structured output prediction problems. Empirical evidence validates…
Department of Mechanical Engineering and Materials Science, Duke University（杜克大学机械工程与材料科学系）；Duke University（杜克大学）
In this paper, we propose a distributed off-policy actor critic method to solve multi-agent reinforcement learning problems. Specifically, we assume that all agents keep local estimates of the global optimal policy parameter and update their local value function estimates independently. Then, we introduce an additional consensus step to let all the agents asymptotically achieve agreement on the global optimal policy function. The convergence analysis of the proposed algorithm is provided and the effectiveness of the proposed algorithm is validated using a distributed resource allocation exampl…
This paper develops the first policy gradient method with global optimality guarantee and complexity analysis for robust reinforcement learning under model mismatch. Robust reinforcement learning is to learn a policy robust to model mismatch between simulator and real environment. We first develop the robust policy (sub-)gradient, which is applicable for any differentiable parametric policy class. We show that the proposed robust policy gradient method converges to the global optimum asymptotically under direct policy parameterization. We further develop a smoothed robust policy gradient metho…
This paper studies a distributed policy gradient in collaborative multi-agent reinforcement learning (MARL), where agents over a communication network aim to find the optimal policy to maximize the average of all agents' local returns. Due to the non-concave performance function of policy gradient, the existing distributed stochastic optimization methods for convex problems cannot be directly used for policy gradient in MARL. This paper proposes a distributed policy gradient with variance reduction and gradient tracking to address the high variances of policy gradient, and utilizes importance …
We introduce Implicit Policy, a general class of expressive policies that can flexibly represent complex action distributions in reinforcement learning, with efficient algorithms to compute entropy regularized policy gradients. We empirically show that, despite its simplicity in implementation, entropy regularization combined with a rich policy class can attain desirable properties displayed under maximum entropy reinforcement learning framework, such as robustness and multi-modality.
University of Edinburgh（爱丁堡大学）；University of Wisconsin – Madison（威斯康星大学麦迪逊分校）
Reinforcement learning (RL) algorithms are often categorized as either on-policy or off-policy depending on whether they use data from a target policy of interest or from a different behavior policy. In this paper, we study a subtle distinction between on-policy data and on-policy sampling in the context of the RL sub-problem of policy evaluation. We observe that on-policy sampling may fail to match the expected distribution of on-policy data after observing only a finite number of trajectories and this failure hinders data-efficient policy evaluation. Towards improved data-efficiency, we show…
Nanjing University（南京大学）；The University of Hong Kong（香港大学）
Value function estimation is an indispensable subroutine in reinforcement learning, which becomes more challenging in the offline setting. In this paper, we propose Hybrid Value Estimation (HVE) to reduce value estimation error, which trades off bias and variance by balancing between the value estimation from offline data and the learned model. Theoretical analysis discloses that HVE enjoys a better error bound than the direct methods. HVE can be leveraged in both off-policy evaluation and offline reinforcement learning settings. We, therefore, provide two concrete algorithms Off-policy HVE (O…
We show how an action-dependent baseline can be used by the policy gradient theorem using function approximation, originally presented with action-independent baselines by (Sutton et al. 2000).
In this paper we present a new way of predicting the performance of a reinforcement learning policy given historical data that may have been generated by a different policy. The ability to evaluate a policy from historical data is important for applications where the deployment of a bad policy can be dangerous or costly. We show empirically that our algorithm produces estimates that often have orders of magnitude lower mean squared error than existing methods---it makes more efficient use of the available data. Our new estimator is based on two advances: an extension of the doubly robust estim…
Policy-based reinforcement learning methods suffer from the policy collapse problem. We find valued-based reinforcement learning methods with ε-greedy mechanism are capable of enjoying three characteristics, Closed-form Diversity, Objective-invariant Exploration and Adaptive Trade-off, which help value-based methods avoid the policy collapse problem. However, there does not exist a parallel mechanism for policy-based methods that achieves all three characteristics. In this paper, we propose an entropy regularization free mechanism that is designed for policy-based methods, which achieves Close…
The performance of reinforcement learning depends upon designing an appropriate action space, where the effect of each action is measurable, yet, granular enough to permit flexible behavior. So far, this process involved non-trivial user choices in terms of the available actions and their execution frequency. We propose a novel framework for reinforcement learning that effectively lifts such constraints. Within our framework, agents learn effective behavior over a routine space: a new, higher-level action space, where each routine represents a set of 'equivalent' sequences of granular actions …
Nara Institute of Science and Technology（奈良先端科学技术大学院大学）
In this paper, we propose cautious policy programming (CPP), a novel value-based reinforcement learning (RL) algorithm that can ensure monotonic policy improvement during learning. Based on the nature of entropy-regularized RL, we derive a new entropy regularization-aware lower bound of policy improvement that only requires estimating the expected policy advantage function. CPP leverages this lower bound as a criterion for adjusting the degree of a policy update for alleviating policy oscillation. Different from similar algorithms that are mostly theory-oriented, we also propose a novel interp…
University of Wisconsin–Madison（威斯康星大学麦迪逊分校）；Microsoft Research New York（微软纽约研究院）
We study a security threat to batch reinforcement learning and control where the attacker aims to poison the learned policy. The victim is a reinforcement learner / controller which first estimates the dynamics and the rewards from a batch data set, and then solves for the optimal policy with respect to the estimates. The attacker can modify the data set slightly before learning happens, and wants to force the learner into learning a target policy chosen by the attacker. We present a unified framework for solving batch policy poisoning attacks, and instantiate the attack on two standard victim…
We obtain global, non-asymptotic convergence guarantees for independent learning algorithms in competitive reinforcement learning settings with two agents (i.e., zero-sum stochastic games). We consider an episodic setting where in each episode, each player independently selects a policy and observes only their own actions and rewards, along with the state. We show that if both players run policy gradient methods in tandem, their policies will converge to a min-max equilibrium of the game, as long as their learning rates follow a two-timescale rule (which is necessary). To the best of our knowl…
Siemens Technology（西门子技术）；Technical University of Munich（慕尼黑工业大学）
In offline reinforcement learning, a policy needs to be learned from a single pre-collected dataset. Typically, policies are thus regularized during training to behave similarly to the data generating policy, by adding a penalty based on a divergence between action distributions of generating and trained policy. We propose a new algorithm, which constrains the policy directly in its weight space instead, and demonstrate its effectiveness in experiments.
Stony Brook University（石溪大学）；Princeton University（普林斯顿大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Northwestern University（西北大学）
This paper extends off-policy reinforcement learning to the multi-agent case in which a set of networked agents communicating with their neighbors according to a time-varying graph collaboratively evaluates and improves a target policy while following a distinct behavior policy. To this end, the paper develops a multi-agent version of emphatic temporal difference learning for off-policy policy evaluation, and proves convergence under linear function approximation. The paper then leverages this result, in conjunction with a novel multi-agent off-policy policy gradient theorem and recent work in…
Carnegie Mellon University（卡内基梅隆大学）；INRIA Lille - Nord Europe（里尔-北欧法国国家信息与自动化研究所）
In some reinforcement learning problems an agent may be provided with a set of input policies, perhaps learned from prior experience or provided by advisors. We present a reinforcement learning with policy advice (RLPA) algorithm which leverages this input set and learns to use the best policy in the set for the reinforcement learning task at hand. We prove that RLPA has a sub-linear regret of \tilde O(\sqrt{T}) relative to the best input policy, and that both this regret and its computational complexity are independent of the size of the state and action space. Our empirical simulations suppo…
Lifelong reinforcement learning provides a promising framework for developing versatile agents that can accumulate knowledge over a lifetime of experience and rapidly learn new tasks by building upon prior knowledge. However, current lifelong learning methods exhibit non-vanishing regret as the amount of experience increases and include limitations that can lead to suboptimal or unsafe control policies. To address these issues, we develop a lifelong policy gradient learner that operates in an adversarial set- ting to learn multiple tasks online while enforcing safety constraints on the learned…
State University of New York at Stony Brook（纽约州立大学石溪分校）；Peking University（北京大学）
Classical reinforcement learning (RL) aims to optimize the expected cumulative rewards. In this work, we consider the RL setting where the goal is to optimize the quantile of the cumulative rewards. We parameterize the policy controlling actions by neural networks and propose a novel policy gradient algorithm called Quantile-Based Policy Optimization (QPO) and its variant Quantile-Based Proximal Policy Optimization (QPPO) to solve deep RL problems with quantile objectives. QPO uses two coupled iterations running at different time scales for simultaneously estimating quantiles and policy parame…
Washington State University（华盛顿州立大学）；Princeton University（普林斯顿大学）
Policy advice is a transfer learning method where a student agent is able to learn faster via advice from a teacher. However, both this and other reinforcement learning transfer methods have little theoretical analysis. This paper formally defines a setting where multiple teacher agents can provide advice to a student and introduces an algorithm to leverage both autonomous exploration and teacher's advice. Our regret bounds justify the intuition that good teachers help while bad teachers hurt. Using our formalization, we are also able to quantify, for the first time, when negative transfer can…
The University of Iowa（爱荷华大学）；National Advanced Driving Simulator, The University of Iowa（爱荷华大学国家高级驾驶模拟器）；Iowa Technology Institute, The University of Iowa（爱荷华大学爱荷华技术研究所）
Intelligent traffic lights in smart cities can optimally reduce traffic congestion. In this study, we employ reinforcement learning to train the control agent of a traffic light on a simulator of urban mobility. As a difference from existing works, a policy-based deep reinforcement learning method, Proximal Policy Optimization (PPO), is utilized other than value-based methods such as Deep Q Network (DQN) and Double DQN (DDQN). At first, the obtained optimal policy from PPO is compared to those from DQN and DDQN. It is found that the policy from PPO performs better than the others. Next, instea…
Recent advances of gradient temporal-difference methods allow to learn off-policy multiple value functions in parallel with- out sacrificing convergence guarantees or computational efficiency. This opens up new possibilities for sound ensemble techniques in reinforcement learning. In this work we propose learning an ensemble of policies related through potential-based shaping rewards. The ensemble induces a combination policy by using a voting mechanism on its components. Learning happens in real time, and we empirically show the combination policy to outperform the individual policies of the …
We have developed a model for online continual or lifelong reinforcement learning (RL) inspired on the insect brain. Our model leverages the offline training of a feature extraction and a common general policy layer to enable the convergence of RL algorithms in online settings. Sharing a common policy layer across tasks leads to positive backward transfer, where the agent continuously improved in older tasks sharing the same underlying general policy. Biologically inspired restrictions to the agent's network are key for the convergence of RL algorithms. This provides a pathway towards efficien…
McGill University（麦吉尔大学）；Mila Québec AI Institute（米拉魁北克人工智能研究所）
Many practical applications of reinforcement learning constrain agents to learn from a fixed batch of data which has already been gathered, without offering further possibility for data collection. In this paper, we demonstrate that due to errors introduced by extrapolation, standard off-policy deep reinforcement learning algorithms, such as DQN and DDPG, are incapable of learning with data uncorrelated to the distribution under the current policy, making them ineffective for this fixed batch setting. We introduce a novel class of off-policy algorithms, batch-constrained reinforcement learning…
Efficient exploration is a crucial challenge in deep reinforcement learning. Several methods, such as behavioral priors, are able to leverage offline data in order to efficiently accelerate reinforcement learning on complex tasks. However, if the task at hand deviates excessively from the demonstrated task, the effectiveness of such methods is limited. In our work, we propose to learn features from offline data that are shared by a more diverse range of tasks, such as correlation between actions and directedness. Therefore, we introduce state-free priors, which directly model temporal consiste…
We present a model-based offline reinforcement learning policy performance lower bound that explicitly captures dynamics model misspecification and distribution mismatch and we propose an empirical algorithm for optimal offline policy selection. Theoretically, we prove a novel safe policy improvement theorem by establishing pessimism approximations to the value function. Our key insight is to jointly consider selecting over dynamics models and policies: as long as a dynamics model can accurately represent the dynamics of the state-action pairs visited by a given policy, it is possible to appro…
Tsinghua University（清华大学）；Carnegie Mellon University（卡内基梅隆大学）；Duke University（杜克大学）；California Institute of Technology（加州理工学院）
We study a multi-agent reinforcement learning (MARL) problem where the agents interact over a given network. The goal of the agents is to cooperatively maximize the average of their entropy-regularized long-term rewards. To overcome the curse of dimensionality and to reduce communication, we propose a Localized Policy Iteration (LPI) algorithm that provably learns a near-globally-optimal policy using only local information. In particular, we show that, despite restricting each agent's attention to only its $κ$-hop neighborhood, the agents are able to learn a policy with an optimality gap that …
The University of Chicago（芝加哥大学）；Princeton University（普林斯顿大学）；Northwestern University（西北大学）
We study the safe reinforcement learning problem with nonlinear function approximation, where policy optimization is formulated as a constrained optimization problem with both the objective and the constraint being nonconvex functions. For such a problem, we construct a sequence of surrogate convex constrained optimization problems by replacing the nonconvex functions locally with convex quadratic functions obtained from policy gradient estimators. We prove that the solutions to these surrogate problems converge to a stationary point of the original nonconvex problem. Furthermore, to extend ou…
This paper studies the adaptive optimal stationary control of continuous-time linear stochastic systems with both additive and multiplicative noises, using reinforcement learning techniques. Based on policy iteration, a novel off-policy reinforcement learning algorithm, named optimistic least-squares-based policy iteration, is proposed which is able to find iteratively near-optimal policies of the adaptive optimal stationary control problem directly from input/state data without explicitly identifying any system matrices, starting from an initial admissible control policy. The solutions given …
Politecnico di Milano（米兰理工大学）；Università di Bologna（博洛尼亚大学）
In reinforcement learning, we encode the potential behaviors of an agent interacting with an environment into an infinite set of policies, the policy space, typically represented by a family of parametric functions. Dealing with such a policy space is a hefty challenge, which often causes sample and computation inefficiencies. However, we argue that a limited number of policies are actually relevant when we also account for the structure of the environment and of the policy parameterization, as many of them would induce very similar interactions, i.e., state-action distributions. In this paper…
Deploying the idea of long-term cumulative return, reinforcement learning has shown remarkable performance in various fields. We propose a formulation of the landmark localization in 3D medical images as a reinforcement learning problem. Whereas value-based methods have been widely used to solve similar problems, we adopt an actor-critic based direct policy search method framed in a temporal difference learning approach. Successful behavior learning is challenging in large state and/or action spaces, requiring many trials. We introduce a partial policy-based reinforcement learning to enable so…
Knowledge Representation is important issue in reinforcement learning. In this paper, we bridge the gap between reinforcement learning and knowledge representation, by providing a rich knowledge representation framework, based on normal logic programs with answer set semantics, that is capable of solving model-free reinforcement learning problems for more complex do-mains and exploits the domain-specific knowledge. We prove the correctness of our approach. We show that the complexity of finding an offline and online policy for a model-free reinforcement learning problem in our approach is NP-c…
University of Cambridge（剑桥大学）；DeepMind；Max Planck Institute（马克斯·普朗克研究所）；Uber AI Labs（Uber人工智能实验室）；UC Berkeley（加州大学伯克利分校）
Off-policy model-free deep reinforcement learning methods using previously collected data can improve sample efficiency over on-policy policy gradient techniques. On the other hand, on-policy algorithms are often more stable and easier to use. This paper examines, both theoretically and empirically, approaches to merging on- and off-policy updates for deep reinforcement learning. Theoretical results show that off-policy updates with a value function estimator can be interpolated with on-policy policy gradient updates whilst still satisfying performance bounds. Our analysis uses control variate…
We propose a method for tackling catastrophic forgetting in deep reinforcement learning that is \textit{agnostic} to the timescale of changes in the distribution of experiences, does not require knowledge of task boundaries, and can adapt in \textit{continuously} changing environments. In our \textit{policy consolidation} model, the policy network interacts with a cascade of hidden networks that simultaneously remember the agent's policy at a range of timescales and regularise the current policy by its own history, thereby improving its ability to learn without forgetting. We find that the mod…
Amazon Web Services（亚马逊云科技）；University of Pennsylvania（宾夕法尼亚大学）
This paper prescribes a suite of techniques for off-policy Reinforcement Learning (RL) that simplify the training process and reduce the sample complexity. First, we show that simple Deterministic Policy Gradient works remarkably well as long as the overestimation bias is controlled. This is contrast to existing literature which creates sophisticated off-policy techniques. Second, we pinpoint training instabilities, typical of off-policy algorithms, to the greedy policy update step; existing solutions such as delayed policy updates do not mitigate this issue. Third, we show that ideas in the p…
Natural policy gradient methods are popular reinforcement learning methods that improve the stability of policy gradient methods by utilizing second-order approximations to precondition the gradient with the inverse of the Fisher-information matrix. However, to the best of the authors' knowledge, there has not been a study that has investigated the effects of different second-order approximations in a comprehensive and systematic manner. To address this, five different second-order approximations were studied and compared across multiple key metrics including performance, stability, sample eff…
Università degli Studi di Firenze（佛罗伦萨大学）；University of Cambridge（剑桥大学）
In this article we study the problem of training intelligent agents using Reinforcement Learning for the purpose of game development. Unlike systems built to replace human players and to achieve super-human performance, our agents aim to produce meaningful interactions with the player, and at the same time demonstrate behavioral traits as desired by game designers. We show how to combine distinct behavioral policies to obtain a meaningful "fusion" policy which comprises all these behaviors. To this end, we propose four different policy fusion methods for combining pre-trained policies. We furt…
Entropy regularization is an important idea in reinforcement learning, with great success in recent algorithms like Soft Q Network (SQN) and Soft Actor-Critic (SAC1). In this work, we extend this idea into the on-policy realm. We propose the soft policy gradient theorem (SPGT) for on-policy maximum entropy reinforcement learning. With SPGT, a series of new policy optimization algorithms are derived, such as SPG, SA2C, SA3C, SDDPG, STRPO, SPPO, SIMPALA and so on. We find that SDDPG is equivalent to SAC1. For policy gradient, the policy network is often represented as a Gaussian distribution wit…
In experimenting with off-policy temporal difference (TD) methods in hierarchical reinforcement learning (HRL) systems, we have observed unwanted on-policy learning under reproducible conditions. Here we present modifications to several TD methods that prevent unintentional on-policy learning from occurring. These modifications create a tension between exploration and learning. Traditional TD methods require commitment to finishing subtasks without exploration in order to update Q-values for early actions with high probability. One-step intra-option learning and temporal second difference trac…
Graduate School of Science and Technology, Nara Institute of Science and Technology（奈良科学技术大学大学院科学技术研究科）
This paper aims to establish an entropy-regularized value-based reinforcement learning method that can ensure the monotonic improvement of policies at each policy update. Unlike previously proposed lower-bounds on policy improvement in general infinite-horizon MDPs, we derive an entropy-regularization aware lower bound. Since our bound only requires the expected policy advantage function to be estimated, it is scalable to large-scale (continuous) state-space problems. We propose a novel reinforcement learning algorithm that exploits this lower-bound as a criterion for adjusting the degree of a…
School of Computer Science, McGill University（麦吉尔大学计算机科学学院）；Department of Electrical, Computer, and Software Engineering, McGill University（麦吉尔大学电气、计算机与软件工程系）
Reinforcement learning has shown promise in learning policies that can solve complex problems. However, manually specifying a good reward function can be difficult, especially for intricate tasks. Inverse reinforcement learning offers a useful paradigm to learn the underlying reward function directly from expert demonstrations. Yet in reality, the corpus of demonstrations may contain trajectories arising from a diverse set of underlying reward functions rather than a single one. Thus, in inverse reinforcement learning, it is useful to consider such a decomposition. The options framework in rei…
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Shenzhen Institute of Artificial Intelligence and Robotics for Society（深圳市人工智能与机器人研究院）
In a sequential decision-making problem, off-policy evaluation estimates the expected cumulative reward of a target policy using logged trajectory data generated from a different behavior policy, without execution of the target policy. Reinforcement learning in high-stake environments, such as healthcare and education, is often limited to off-policy settings due to safety or ethical concerns, or inability of exploration. Hence it is imperative to quantify the uncertainty of the off-policy estimate before deployment of the target policy. In this paper, we propose a novel framework that provides…
