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1. Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes

   Kallus, Nathan; Uehara, Masatoshi (January 2020, Journal of machine learning research)

   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 is efficient when both components are estimated at fourth-root rates and is also doubly robust when only one component is consistent. We investigate these properties empirically and demonstrate the performance benefits due to harnessing memorylessness. 

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2. Towards optimal off-policy evaluation for reinforcement learning with marginalized importance sampling.

   Xie, T.; Ma, Y.; Wang, Y. X. (January 2019, Advances in neural information processing systems)

   Motivated by the many real-world applications of reinforcement learning (RL) that require safe-policy iterations, we consider the problem of off-policy evaluation (OPE) — the problem of evaluating a new policy using the historical data ob- tained by different behavior policies — under the model of nonstationary episodic Markov Decision Processes (MDP) with a long horizon and a large action space. Existing importance sampling (IS) methods often suffer from large variance that depends exponentially on the RL horizon H. To solve this problem, we consider a marginalized importance sampling (MIS) estimator that recursively estimates the state marginal distribution for the target policy at every step. MIS achieves a mean-squared error of [ ] where μ and π are the logging and target policies, dμt (st) and dπt (st) are the marginal distribution of the state at tth step, H is the horizon, n is the sample size and V π is the value function of the MDP under π. The result matches the t+1 Cramer-Rao lower bound in Jiang and Li [2016] up to a multiplicative factor of H. To the best of our knowledge, this is the first OPE estimation error bound with a polynomial dependence on H . Besides theory, we show empirical superiority of our method in time-varying, partially observable, and long-horizon RL environments. 

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3. A Minimax Learning Approach to Off-Policy Evaluation in Confounded Partially Observable Markov Decision Processes

   Shi, Chengchun; Uehara, Masatoshi; Huang, Jiawei; Jiang, Nan (July 2022, Proceedings of the 39th International Conference on Machine Learning)

   We consider off-policy evaluation (OPE) in Partially Observable Markov Decision Processes (POMDPs), where the evaluation policy depends only on observable variables and the behavior policy depends on unobservable latent variables. Existing works either assume no unmeasured confounders, or focus on settings where both the observation and the state spaces are tabular. In this work, we first propose novel identification methods for OPE in POMDPs with latent confounders, by introducing bridge functions that link the target policy’s value and the observed data distribution. We next propose minimax estimation methods for learning these bridge functions, and construct three estimators based on these estimated bridge functions, corresponding to a value function-based estimator, a marginalized importance sampling estimator, and a doubly-robust estimator. Our proposal permits general function approximation and is thus applicable to settings with continuous or large observation/state spaces. The nonasymptotic and asymptotic properties of the proposed estimators are investigated in detail. A Python implementation of our proposal is available at https://github.com/jiaweihhuang/ Confounded-POMDP-Exp. 

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4. Get a Head Start: On-Demand Pedagogical Policy Selection in Intelligent Tutoring

   Gao, G; Yang, X; Chi, M (February 2024, AAAI)

   Reinforcement learning (RL) is broadly employed in humaninvolved systems to enhance human outcomes. Off-policy evaluation (OPE) has been pivotal for RL in those realms since online policy learning and evaluation can be high-stake. Intelligent tutoring has raised tremendous attentions as highly challenging when applying OPE to human-involved systems, due to that students’ subgroups can favor different pedagogical policies and the costly procedure that policies have to be induced fully offline and then directly deployed to the upcoming semester. In this work, we formulate on-demand pedagogical policy selection (ODPS) to tackle the challenges for OPE in intelligent tutoring. We propose a pipeline, EDUPLANNER, as a concrete solution for ODPS. Our pipeline results in an theoretically unbiased estimator, and enables efficient and customized policy selection by identifying subgroups over both historical data and on-arrival initial logs. We evaluate our approach on the Probability ITS that has been used in real classrooms for over eight years. Our study shows significant improvement on learning outcomes of students with EDUPLANNER, especially for the ones associated with low-performing subgroups. 

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5. Future-Dependent Value-Based Off-Policy Evaluation in POMDPs

   Uehara, Masatoshi; Kiyohara, Haruka; Bennett, Andrew; Chernozhukov, Victor; Jiang, Nan; Kallus, Nathan; Shi, Chengchun; Sun, Wen (December 2023, Neural Information Processing Systems (NeurIPS 2023))

   We study off-policy evaluation (OPE) for partially observable MDPs (POMDPs) with general function approximation. Existing methods such as sequential im- portance sampling estimators suffer from the curse of horizon in POMDPs. To circumvent this problem, we develop a novel model-free OPE method by introduc- ing future-dependent value functions that take future proxies as inputs and perform a similar role to that of classical value functions in fully-observable MDPs. We derive a new off-policy Bellman equation for future-dependent value functions as conditional moment equations that use history proxies as instrumental variables. We further propose a minimax learning method to learn future-dependent value functions using the new Bellman equation. We obtain the PAC result, which implies our OPE estimator is close to the true policy value under Bellman completeness, as long as futures and histories contain sufficient information about latent states. 

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