We study the problem of off-policy evaluation (OPE) in reinforcement learning (RL), where the goal is to estimate the performance of a policy from the data generated by another policy(ies). In particular, we focus on the doubly robust (DR) estimators that consist of an importance sampling (IS) component and a performance model, and utilize the low (or zero) bias of IS and low variance of the model at the same time. Although the accuracy of the model has a huge impact on the overall performance of DR, most of the work on using the DR estimators in OPE has been focused on improving the IS part, and not much on how to learn the model. In this paper, we propose alternative DR estimators, called more robust doubly robust (MRDR), that learn the model parameter by minimizing the variance of the DR estimator. We first present a formulation for learning the DR model in RL. We then derive formulas for the variance of the DR estimator in both contextual bandits and RL, such that their gradients w.r.t.~the model parameters can be estimated from the samples, and propose methods to efficiently minimize the variance. We prove that the MRDR estimators are strongly consistent and asymptotically optimal. Finally, we evaluate MRDR in bandits and RL benchmark problems, and compare its performance with the existing methods.
We study sequential decision making in environments where rewards are only partially observed, but can be modeled as a function of observed contexts and the chosen action by the decision maker. This setting, known as contextual bandits, encompasses a wide variety of applications such as health care, content recommendation and Internet advertising. A central task is evaluation of a new policy given historic data consisting of contexts, actions and received rewards. The key challenge is that the past data typically does not faithfully represent proportions of actions taken by a new policy. Previ…
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…
Off-policy evaluation (OPE) in reinforcement learning allows one to evaluate novel decision policies without needing to conduct exploration, which is often costly or otherwise infeasible. We consider for the first time the semiparametric efficiency limits of OPE in Markov decision processes (MDPs), where actions, rewards, and states are memoryless. We show existing OPE estimators may fail to be efficient in this setting. We develop a new estimator based on cross-fold estimation of $q$-functions and marginalized density ratios, which we term double reinforcement learning (DRL). We show that DRL…
Low Variance Off-policy Evaluation with State-based Importance Sampling
Agency for Science, Technology and Research（新加坡科技研究局）；Manning College of Information and Computer Sciences（曼宁信息与计算机科学学院）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）
Off-OAB: Off-Policy Policy Gradient Method with Optimal Action-Dependent Baseline
School of Software, Shandong University（山东大学软件学院）；School of Artificial Intelligence, Peking University（北京大学人工智能学院）；College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）
University of Oxford（牛津大学）；University of Alberta（阿尔伯塔大学）
We consider off-policy policy evaluation with function approximation (FA) in average-reward MDPs, where the goal is to estimate both the reward rate and the differential value function. For this problem, bootstrapping is necessary and, along with off-policy learning and FA, results in the deadly triad (Sutton & Barto, 2018). To address the deadly triad, we propose two novel algorithms, reproducing the celebrated success of Gradient TD algorithms in the average-reward setting. In terms of estimating the differential value function, the algorithms are the first convergent off-policy linear funct…
In the framework of Markov Decision Processes, off-policy learning, that is the problem of learning a linear approximation of the value function of some fixed policy from one trajectory possibly generated by some other policy. We briefly review on-policy learning algorithms of the literature (gradient-based and least-squares-based), adopting a unified algorithmic view. Then, we highlight a systematic approach for adapting them to off-policy learning with eligibility traces. This leads to some known algorithms - off-policy LSTD(λ), LSPE(λ), TD(λ), TDC/GQ(λ) - and suggests new extensions - off-p…
Offline-Boosted Actor-Critic: Adaptively Blending Optimal Historical Behaviors in Deep Off-Policy RL
Tsinghua University（清华大学）；University of Hamburg（汉堡大学）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；Shanghai Qi Zhi Institute（上海期智研究院）；Institute for AI Industry Research, Tsinghua University（清华大学人工智能产业研究院）
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）
Offline reinforcement learning (RL), also known as batch RL, aims to optimize policy from a large pre-recorded dataset without interaction with the environment. This setting offers the promise of utilizing diverse, pre-collected datasets to obtain policies without costly, risky, active exploration. However, commonly used off-policy algorithms based on Q-learning or actor-critic perform poorly when learning from a static dataset. In this work, we study why off-policy RL methods fail to learn in offline setting from the value function view, and we propose a novel offline RL algorithm that we cal…
Monotonic policy improvement and off-policy learning are two main desirable properties for reinforcement learning algorithms. In this paper, by lower bounding the performance difference of two policies, we show that the monotonic policy improvement is guaranteed from on- and off-policy mixture samples. An optimization procedure which applies the proposed bound can be regarded as an off-policy natural policy gradient method. In order to support the theoretical result, we provide a trust region policy optimization method using experience replay as a naive application of our bound, and evaluate i…
We study the problem of off-policy policy optimization in Markov decision processes, and develop a novel off-policy policy gradient method. Prior off-policy policy gradient approaches have generally ignored the mismatch between the distribution of states visited under the behavior policy used to collect data, and what would be the distribution of states under the learned policy. Here we build on recent progress for estimating the ratio of the state distributions under behavior and evaluation policies for policy evaluation, and present an off-policy policy gradient optimization technique that 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…
Facebook AI Research（脸书人工智能研究院）；McGill University（麦吉尔大学）
Off-policy deep reinforcement learning (RL) algorithms are incapable of learning solely from batch offline data without online interactions with the environment, due to the phenomenon known as \textit{extrapolation error}. This is often due to past data available in the replay buffer that may be quite different from the data distribution under the current policy. We argue that most off-policy learning methods fundamentally suffer from a \textit{state distribution shift} due to the mismatch between the state visitation distribution of the data collected by the behavior and target policies. This…
We propose a new objective, the counterfactual objective, unifying existing objectives for off-policy policy gradient algorithms in the continuing reinforcement learning (RL) setting. Compared to the commonly used excursion objective, which can be misleading about the performance of the target policy when deployed, our new objective better predicts such performance. We prove the Generalized Off-Policy Policy Gradient Theorem to compute the policy gradient of the counterfactual objective and use an emphatic approach to get an unbiased sample from this policy gradient, yielding the Generalized O…
Learning a goal-oriented dialog policy is generally performed offline with supervised learning algorithms or online with reinforcement learning (RL). Additionally, as companies accumulate massive quantities of dialog transcripts between customers and trained human agents, encoder-decoder methods have gained popularity as agent utterances can be directly treated as supervision without the need for utterance-level annotations. However, one potential drawback of such approaches is that they myopically generate the next agent utterance without regard for dialog-level considerations. To resolve thi…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Carnegie Mellon University（卡内基梅隆大学）；Purdue University（普渡大学）
Addressing such diverse ends as safety alignment with human preferences, and the efficiency of learning, a growing line of reinforcement learning research focuses on risk functionals that depend on the entire distribution of returns. Recent work on \emph{off-policy risk assessment} (OPRA) for contextual bandits introduced consistent estimators for the target policy's CDF of returns along with finite sample guarantees that extend to (and hold simultaneously over) all risk. In this paper, we lift OPRA to Markov decision processes (MDPs), where importance sampling (IS) CDF estimators suffer high …
University of Texas at Austin（得克萨斯大学奥斯汀分校）；Google Research（谷歌研究院）
Infinite horizon off-policy policy evaluation is a highly challenging task due to the excessively large variance of typical importance sampling (IS) estimators. Recently, Liu et al. (2018a) proposed an approach that significantly reduces the variance of infinite-horizon off-policy evaluation by estimating the stationary density ratio, but at the cost of introducing potentially high biases due to the error in density ratio estimation. In this paper, we develop a bias-reduced augmentation of their method, which can take advantage of a learned value function to obtain higher accuracy. Our method …
We study decision making in environments where the reward is only partially observed, but can be modeled as a function of an action and an observed context. This setting, known as contextual bandits, encompasses a wide variety of applications including health-care policy and Internet advertising. A central task is evaluation of a new policy given historic data consisting of contexts, actions and received rewards. The key challenge is that the past data typically does not faithfully represent proportions of actions taken by a new policy. Previous approaches rely either on models of rewards or m…
This work studies the problem of batch off-policy evaluation for Reinforcement Learning in partially observable environments. Off-policy evaluation under partial observability is inherently prone to bias, with risk of arbitrarily large errors. We define the problem of off-policy evaluation for Partially Observable Markov Decision Processes (POMDPs) and establish what we believe is the first off-policy evaluation result for POMDPs. In addition, we formulate a model in which observed and unobserved variables are decoupled into two dynamic processes, called a Decoupled POMDP. We show how off-poli…
Department of Statistics（统计系）；LSE London, UK（伦敦大学学院）；Department of Mathematics（数学系）；Tsinghua University（清华大学）；School of Design LCC, UAL London, UK（伦敦艺术大学设计学院）；Department of Engineering Science（工程科学系）；University of Oxford（牛津大学）
Cost-optimal Sequential Testing via Doubly Robust Q-learning
Department of Statistics and Data Science, National University of Singapore（国立新加坡大学统计与数据科学系）；Public Health Sciences Division, Fred Hutch（Fred Hutch公共卫生科学系）；Department of Biomedical Data Science, Stanford University School of Medicine（斯坦福大学医学院生物医学数据科学系）；Department of Biostatistics, Harvard T.H. Chan School of Public Health（哈佛大学T.H. Chan公共卫生学院生物统计学系）
Nara Institute of Science and Technology（奈良先端科学技术大学院大学）
The oscillating performance of off-policy learning and persisting errors in the actor-critic (AC) setting call for algorithms that can conservatively learn to suit the stability-critical applications better. In this paper, we propose a novel off-policy AC algorithm cautious actor-critic (CAC). The name cautious comes from the doubly conservative nature that we exploit the classic policy interpolation from conservative policy iteration for the actor and the entropy-regularization of conservative value iteration for the critic. Our key observation is the entropy-regularized critic facilitates an…
Off-policy learning refers to the problem of learning the value function of a way of behaving, or policy, while following a different policy. Gradient-based off-policy learning algorithms, such as GTD and TDC/GQ, converge even when using function approximation and incremental updates. However, they have been developed for the case of a fixed behavior policy. In control problems, one would like to adapt the behavior policy over time to become more greedy with respect to the existing value function. In this paper, we present the first gradient-based learning algorithms for this problem, which re…
Specifying reward functions for complex tasks like object manipulation or driving is challenging to do by hand. Reward learning seeks to address this by learning a reward model using human feedback on selected query policies. This shifts the burden of reward specification to the optimal design of the queries. We propose a theoretical framework for studying reward learning and the associated optimal experiment design problem. Our framework models rewards and policies as nonparametric functions belonging to subsets of Reproducing Kernel Hilbert Spaces (RKHSs). The learner receives (noisy) oracle…
We propose and analyze an alternate approach to off-policy multi-step temporal difference learning, in which off-policy returns are corrected with the current Q-function in terms of rewards, rather than with the target policy in terms of transition probabilities. We prove that such approximate corrections are sufficient for off-policy convergence both in policy evaluation and control, provided certain conditions. These conditions relate the distance between the target and behavior policies, the eligibility trace parameter and the discount factor, and formalize an underlying tradeoff in off-pol…
Randomized trials, also known as A/B tests, are used to select between two policies: a control and a treatment. Given a corresponding set of features, we can ideally learn an optimized policy P that maps the A/B test data features to action space and optimizes reward. However, although A/B testing provides an unbiased estimator for the value of deploying B (i.e., switching from policy A to B), direct application of those samples to learn the the optimized policy P generally does not provide an unbiased estimator of the value of P as the samples were observed when constructing P. In situations …
