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1. Learning Bellman Complete Representations for Offline Policy Evaluation

   Jonathan Chang, Kaiwen Wang (January 2022, Proceedings of the 39th International Conference on Machine Learning)

   We study representation learning for Offline Reinforcement Learning (RL), focusing on the important task of Offline Policy Evaluation (OPE). Recent work shows that, in contrast to supervised learning, realizability of the Q-function is not enough for learning it. Two sufficient conditions for sample-efficient OPE are Bellman completeness and coverage. Prior work often assumes that representations satisfying these conditions are given, with results being mostly theoretical in nature. In this work, we propose BCRL, which directly learns from data an approximately linear Bellman complete representation with good coverage. With this learned representation, we perform OPE using Least Square Policy Evaluation (LSPE) with linear functions in our learned representation. We present an end-to-end theoretical analysis, showing that our two-stage algorithm enjoys polynomial sample complexity provided some representation in the rich class considered is linear Bellman complete. Empirically, we extensively evaluate our algorithm on challenging, image-based continuous control tasks from the Deepmind Control Suite. We show our representation enables better OPE compared to previous representation learning methods developed for off-policy RL (e.g., CURL, SPR). BCRL achieve competitive OPE error with the state-of-the-art method Fitted Q-Evaluation (FQE), and beats FQE when evaluating beyond the initial state distribution. Our ablations show that both linear Bellman complete and coverage components of our method are crucial. 

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2. 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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3. Offline Reinforcement Learning with Realizability and Single-policy Concentrability

   Zhan, Wenhao; Huang, Baihe; Huang, Audrey; Jiang, Nan; Lee, Jason (July 2022, Proceedings of Thirty Fifth Conference on Learning Theory)

   Sample-efficiency guarantees for offline reinforcement learning (RL) often rely on strong assumptions on both the function classes (e.g., Bellman-completeness) and the data coverage (e.g., all-policy concentrability). Despite the recent efforts on relaxing these assumptions, existing works are only able to relax one of the two factors, leaving the strong assumption on the other factor intact. As an important open problem, can we achieve sample-efficient offline RL with weak assumptions on both factors? In this paper we answer the question in the positive. We analyze a simple algorithm based on the primal-dual formulation of MDPs, where the dual variables (discounted occupancy) are modeled using a density-ratio function against offline data. With proper regularization, the algorithm enjoys polynomial sample complexity, under only realizability and single-policy concentrability. We also provide alternative analyses based on different assumptions to shed light on the nature of primal-dual algorithms for offline RL. 

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4. What are the Statistical Limits of Offline RL with Linear Function Approximation?

   Wang, Ruosong; Foster, Dean; Kakade, Sham M. (January 2021, International Conference on Learning Representations)

   Offline reinforcement learning seeks to utilize offline (observational) data to guide the learning of (causal) sequential decision making strategies. The hope is that offline reinforcement learning coupled with function approximation methods (to deal with the curse of dimensionality) can provide a means to help alleviate the excessive sample complexity burden in modern sequential decision making problems. However, the extent to which this broader approach can be effective is not well understood, where the literature largely consists of sufficient conditions. This work focuses on the basic question of what are necessary representational and distributional conditions that permit provable sample-efficient offline reinforcement learning. Perhaps surprisingly, our main result shows that even if: i) we have realizability in that the true value function of \emph{every} policy is linear in a given set of features and 2) our off-policy data has good coverage over all features (under a strong spectral condition), any algorithm still (information-theoretically) requires a number of offline samples that is exponential in the problem horizon to non-trivially estimate the value of \emph{any} given policy. Our results highlight that sample-efficient offline policy evaluation is not possible unless significantly stronger conditions hold; such conditions include either having low distribution shift (where the offline data distribution is close to the distribution of the policy to be evaluated) or significantly stronger representational conditions (beyond realizability). 

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5. Gradientdice: Rethinking generalized offline estimation of stationary values.

   Zhang, S; B, Liu; Whiteson, S. (July 2020, International Conference on Machine Learning)

   We present GradientDICE for estimating the density ratio between the state distribution of the target policy and the sampling distribution in off-policy reinforcement learning. GradientDICE fixes several problems of GenDICE (Zhang et al.,2020a), the state-of-the-art for estimating such density ratios. Namely, the optimization problem in GenDICE is not a convex-concave saddle-point problem once nonlinearity in optimization variable parameterization is introduced to ensure positivity, so any primal-dual algorithm is not guaranteed to converge or find the desired solution. However, such nonlinearity is essential to ensure the consistency of GenDICE even with a tabular representation. This is a fundamental contradiction, resulting from GenDICE’s original formulation of the optimization problem. In GradientDICE, we optimize a different objective from GenDICE by using the Perron-Frobenius theorem and eliminating GenDICE’s use of divergence. Consequently, nonlinearity in parameterization is not necessary for GradientDICE, which is provably convergent under linear function approximation. 

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