Off-policy evaluation of sequential decision policies from observational data is necessary in applications of batch reinforcement learning such as education and healthcare. In such settings, however, unobserved variables confound observed actions, rendering exact evaluation of new policies impossible, i.e., unidentifiable. We develop a robust approach that estimates sharp bounds on the (unidentifiable) value of a given policy in an infinite-horizon problem given data from another policy with unobserved confounding, subject to a sensitivity model. We consider stationary or baseline unobserved confounding and compute bounds by optimizing over the set of all stationary state-occupancy ratios that agree with a new partially identified estimating equation and the sensitivity model. We prove convergence to the sharp bounds as we collect more confounded data. Although checking set membership is a linear program, the support function is given by a difficult nonconvex optimization problem. We develop approximations based on nonconvex projected gradient descent and demonstrate the resulting bounds empirically.
When observed decisions depend only on observed features, off-policy policy evaluation (OPE) methods for sequential decision making problems can estimate the performance of evaluation policies before deploying them. This assumption is frequently violated due to unobserved confounders, unrecorded variables that impact both the decisions and their outcomes. We assess robustness of OPE methods under unobserved confounding by developing worst-case bounds on the performance of an evaluation policy. When unobserved confounders can affect every decision in an episode, we demonstrate that even small a…
We study the offline contextual bandit problem, where we aim to acquire an optimal policy using observational data. However, this data usually contains two deficiencies: (i) some variables that confound actions are not observed, and (ii) missing observations exist in the collected data. Unobserved confounders lead to a confounding bias and missing observations cause bias and inefficiency problems. To overcome these challenges and learn the optimal policy from the observed dataset, we present a new algorithm called Causal-Adjusted Pessimistic (CAP) policy learning, which forms the reward functi…
A Convex Framework for Confounding Robust Inference
Department of Mathematics ETH Zurich（苏黎世联邦理工学院数学系）；Department of Computer Science ETH Zurich（苏黎世联邦理工学院计算机科学系）；School of Computing Institute of Science Tokyo（东京科学大学计算学部）；RIKEN AIP（日本理化学研究所AIP）
Reinforcement Learning with Continuous Actions Under Unmeasured Confounding
Department of Statistics, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校统计学系）；Department of Human Development and Family Studies, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校人类发展与家庭研究系）；Department of Statistics, University of California Irvine（加州大学尔湾分校统计学系）；Department of Decision Sciences, The George Washington University（乔治华盛顿大学决策科学系）；School of Management & Center for Data Science, Zhejiang University（浙江大学管理学院及数据科学中心）
We show that the popular reinforcement learning (RL) strategy of estimating the state-action value (Q-function) by minimizing the mean squared Bellman error leads to a regression problem with confounding, the inputs and output noise being correlated. Hence, direct minimization of the Bellman error can result in significantly biased Q-function estimates. We explain why fixing the target Q-network in Deep Q-Networks and Fitted Q Evaluation provides a way of overcoming this confounding, thus shedding new light on this popular but not well understood trick in the deep RL literature. An alternative…
Northwestern University（西北大学）；George Washington University（乔治华盛顿大学）；Yale University（耶鲁大学）；University of Miami（迈阿密大学）
Motivated by the human-machine interaction such as training chatbots for improving customer satisfaction, we study human-guided human-machine interaction involving private information. We model this interaction as a two-player turn-based game, where one player (Alice, a human) guides the other player (Bob, a machine) towards a common goal. Specifically, we focus on offline reinforcement learning (RL) in this game, where the goal is to find a policy pair for Alice and Bob that maximizes their expected total rewards based on an offline dataset collected a priori. The offline setting presents two…
Causal Flow Q-Learning for Robust Offline Reinforcement Learning
Causal AI Lab, Columbia University, NY, United States（因果AI实验室，哥伦比亚大学，纽约，美国）；Department of Electrical Engineering and Computer Science, Syracuse University, NY, United States（电气工程与计算机科学系，雪城大学，纽约，美国）
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；East China Normal University（华东师范大学）；University of Science and Technology of China（中国科学技术大学）；Shandong University（山东大学）；Georgia Institute of Technology（佐治亚理工学院）
We consider off-policy policy evaluation when the trajectory data are generated by multiple behavior policies. Recent work has shown the key role played by the state or state-action stationary distribution corrections in the infinite horizon context for off-policy policy evaluation. We propose estimated mixture policy (EMP), a novel class of partially policy-agnostic methods to accurately estimate those quantities. With careful analysis, we show that EMP gives rise to estimates with reduced variance for estimating the state stationary distribution correction while it also offers a useful induc…
Off-policy evaluation (OPE) in reinforcement learning is notoriously difficult in long- and infinite-horizon settings due to diminishing overlap between behavior and target policies. In this paper, we study the role of Markovian and time-invariant structure in efficient OPE. We first derive the efficiency bounds for OPE when one assumes each of these structures. This precisely characterizes the curse of horizon: in time-variant processes, OPE is only feasible in the near-on-policy setting, where behavior and target policies are sufficiently similar. But, in time-invariant Markov decision proce…
Stanford University（斯坦福大学）；Mila - University of Montreal（米拉研究所 - 蒙特利尔大学）
Off-policy policy estimators that use importance sampling (IS) can suffer from high variance in long-horizon domains, and there has been particular excitement over new IS methods that leverage the structure of Markov decision processes. We analyze the variance of the most popular approaches through the viewpoint of conditional Monte Carlo. Surprisingly, we find that in finite horizon MDPs there is no strict variance reduction of per-decision importance sampling or stationary importance sampling, comparing with vanilla importance sampling. We then provide sufficient conditions under which the p…
KLATASDS - MOE School of Statistics East China Normal University（KLATASDS - 教育部统计学系华东师范大学）
Reliable uncertainty quantification is crucial for reinforcement learning (RL) in high-stakes settings. We propose a unified conformal prediction framework for infinite-horizon policy evaluation that constructs distribution-free prediction intervals {for returns} in both on-policy and off-policy settings. Our method integrates distributional RL with conformal calibration, addressing challenges such as unobserved returns, temporal dependencies, and distributional shifts. We propose a modular pseudo-return construction based on truncated rollouts and a time-aware calibration strategy using exper…
Confounding Masquerading as Improvement: A Systematic Evaluation of Offline Reinforcement Learning for Stroke Antithrombotic Treatment in a 129,000-Patient Registry
We study the problem of learning personalized decision policies from observational data while accounting for possible unobserved confounding. Previous approaches, which assume unconfoundedness, i.e., that no unobserved confounders affect both the treatment assignment as well as outcome, can lead to policies that introduce harm rather than benefit when some unobserved confounding is present, as is generally the case with observational data. Instead, since policy value and regret may not be point-identifiable, we study a method that minimizes the worst-case estimated regret of a candidate policy…
Carnegie Mellon University（卡内基梅隆大学）；Georgia Institute of Technology（佐治亚理工学院）
In this paper, we propose to combine imitation and reinforcement learning via the idea of reward shaping using an oracle. We study the effectiveness of the near-optimal cost-to-go oracle on the planning horizon and demonstrate that the cost-to-go oracle shortens the learner's planning horizon as function of its accuracy: a globally optimal oracle can shorten the planning horizon to one, leading to a one-step greedy Markov Decision Process which is much easier to optimize, while an oracle that is far away from the optimality requires planning over a longer horizon to achieve near-optimal perfor…
Off-policy evaluation (OPE) in reinforcement learning is an important problem in settings where experimentation is limited, such as education and healthcare. But, in these very same settings, observed actions are often confounded by unobserved variables making OPE even more difficult. We study an OPE problem in an infinite-horizon, ergodic Markov decision process with unobserved confounders, where states and actions can act as proxies for the unobserved confounders. We show how, given only a latent variable model for states and actions, policy value can be identified from off-policy data. Our …
Off-policy estimation for long-horizon problems is important in many real-life applications such as healthcare and robotics, where high-fidelity simulators may not be available and on-policy evaluation is expensive or impossible. Recently, \cite{liu18breaking} proposed an approach that avoids the \emph{curse of horizon} suffered by typical importance-sampling-based methods. While showing promising results, this approach is limited in practice as it requires data be drawn from the \emph{stationary distribution} of a \emph{known} behavior policy. In this work, we propose a novel approach that el…
We present relay policy learning, a method for imitation and reinforcement learning that can solve multi-stage, long-horizon robotic tasks. This general and universally-applicable, two-phase approach consists of an imitation learning stage that produces goal-conditioned hierarchical policies, and a reinforcement learning phase that finetunes these policies for task performance. Our method, while not necessarily perfect at imitation learning, is very amenable to further improvement via environment interaction, allowing it to scale to challenging long-horizon tasks. We simplify the long-horizon …
Automatic Reward Shaping from Confounded Offline Data
Causal AI Lab, Columbia University, New York, USA（因果AI实验室，哥伦比亚大学，纽约，美国）；Department of Electrical Engineering and Computer Science, Syracuse University, New York, USA（电气工程与计算机科学系， Syracuse大学，纽约，美国）
We study off-policy evaluation and learning from sequential data in a structured class of Markov decision processes that arise from repeated interactions with an exogenous sequence of arrivals with contexts, which generate unknown individual-level responses to agent actions. This model can be thought of as an offline generalization of contextual bandits with resource constraints. We formalize the relevant causal structure of problems such as dynamic personalized pricing and other operations management problems in the presence of potentially high-dimensional user types. The key insight is that …
In applications of offline reinforcement learning to observational data, such as in healthcare or education, a general concern is that observed actions might be affected by unobserved factors, inducing confounding and biasing estimates derived under the assumption of a perfect Markov decision process (MDP) model. Here we tackle this by considering off-policy evaluation in a partially observed MDP (POMDP). Specifically, we consider estimating the value of a given target policy in a POMDP given trajectories with only partial state observations generated by a different and unknown policy that may…
The Ohio State University（俄亥俄州立大学）；The Ohio State University Wexner Medical Center（俄亥俄州立大学韦克斯纳医学中心）
Despite intense efforts in basic and clinical research, an individualized ventilation strategy for critically ill patients remains a major challenge. Recently, dynamic treatment regime (DTR) with reinforcement learning (RL) on electronic health records (EHR) has attracted interest from both the healthcare industry and machine learning research community. However, most learned DTR policies might be biased due to the existence of confounders. Although some treatment actions non-survivors received may be helpful, if confounders cause the mortality, the training of RL models guided by long-term ou…
University of Oxford（牛津大学）；London School of Economics and Political Science（伦敦政治经济学院）
Despite its popularity in the reinforcement learning community, a provably convergent policy gradient method for continuous space-time control problems with nonlinear state dynamics has been elusive. This paper proposes proximal gradient algorithms for feedback controls of finite-time horizon stochastic control problems. The state dynamics are nonlinear diffusions with control-affine drift, and the cost functions are nonconvex in the state and nonsmooth in the control. The system noise can degenerate, which allows for deterministic control problems as special cases. We prove under suitable con…
Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学研究所）；UCLA（加州大学洛杉矶分校）
We consider the problem of finding the best memoryless stochastic policy for an infinite-horizon partially observable Markov decision process (POMDP) with finite state and action spaces with respect to either the discounted or mean reward criterion. We show that the (discounted) state-action frequencies and the expected cumulative reward are rational functions of the policy, whereby the degree is determined by the degree of partial observability. We then describe the optimization problem as a linear optimization problem in the space of feasible state-action frequencies subject to polynomial co…
Off-policy evaluation in reinforcement learning offers the chance of using observational data to improve future outcomes in domains such as healthcare and education, but safe deployment in high stakes settings requires ways of assessing its validity. Traditional measures such as confidence intervals may be insufficient due to noise, limited data and confounding. In this paper we develop a method that could serve as a hybrid human-AI system, to enable human experts to analyze the validity of policy evaluation estimates. This is accomplished by highlighting observations in the data whose removal…
Blessing from Human-AI Interaction: Super Reinforcement Learning in Confounded Environments
Department of Mathematical Sciences, University of Texas at Dallas（德克萨斯大学达拉斯分校数学科学系）；Department of Statistics, London School of Economics and Political Science（伦敦政治经济学院统计系）；Department of Decision Sciences, George Washington University（乔治华盛顿大学决策科学系）
When designing algorithms for finite-time-horizon episodic reinforcement learning problems, a common approach is to introduce a fictitious discount factor and use stationary policies for approximations. Empirically, it has been shown that the fictitious discount factor helps reduce variance, and stationary policies serve to save the per-iteration computational cost. Theoretically, however, there is no existing work on convergence analysis for algorithms with this fictitious discount recipe. This paper takes the first step towards analyzing these algorithms. It focuses on two vanilla policy gra…
Center for Smart Health, University of California, Los Angeles（加州大学洛杉矶分校智能健康中心）
A data science task can be deemed as making sense of the data or testing a hypothesis about it. The conclusions inferred from data can greatly guide us to make informative decisions. Big data has enabled us to carry out countless prediction tasks in conjunction with machine learning, such as identifying high risk patients suffering from a certain disease and taking preventable measures. However, healthcare practitioners are not content with mere predictions - they are also interested in the cause-effect relation between input features and clinical outcomes. Understanding such relations will he…
We explore reinforcement learning methods for finding the optimal policy in the linear quadratic regulator (LQR) problem. In particular, we consider the convergence of policy gradient methods in the setting of known and unknown parameters. We are able to produce a global linear convergence guarantee for this approach in the setting of finite time horizon and stochastic state dynamics under weak assumptions. The convergence of a projected policy gradient method is also established in order to handle problems with constraints. We illustrate the performance of the algorithm with two examples. The…
