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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Bellman Residual Orthogonalization for Offline Reinforcement Learning
We propose and analyze a reinforcement learning principle that
approximates the Bellman equations by enforcing their validity only
along an user-defined space of test functions. Focusing on
applications to model-free offline RL with function approximation, we
exploit this principle to derive confidence intervals for off-policy
evaluation, as well as to optimize over policies within a prescribed
policy class. We prove an oracle inequality on our policy optimization
procedure in terms of a trade-off between the value and uncertainty of
an arbitrary comparator policy. Different choices of test function
spaces allow us to tackle different problems within a common
framework. We characterize the loss of efficiency in moving from
on-policy to off-policy data using our procedures, and establish
connections to concentrability coefficients studied in past work. We
examine in depth the implementation of our methods with linear
function approximation, and provide theoretical guarantees with
polynomial-time implementations even when Bellman closure does not
hold.
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- NSF-PAR ID:
- 10343719
- Date Published:
- Journal Name:
- ArXivorg
- ISSN:
- 2331-8422
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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