Offline Minimax Soft-Q-learning Under Realizability and Partial Coverage

• URL: http://arxiv.org/abs/2302.02392v2
• Date: Mon, 13 Nov 2023 14:46:44 GMT
• Title: Offline Minimax Soft-Q-learning Under Realizability and Partial Coverage
• Authors: Masatoshi Uehara, Nathan Kallus, Jason D. Lee, Wen Sun
• Abstract summary: We propose value-based algorithms for offline reinforcement learning (RL) We show an analogous result for vanilla Q-functions under a soft margin condition. Our algorithms' loss functions arise from casting the estimation problems as nonlinear convex optimization problems and Lagrangifying.
• Score: 100.8180383245813
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In offline reinforcement learning (RL) we have no opportunity to explore so we must make assumptions that the data is sufficient to guide picking a good policy, taking the form of assuming some coverage, realizability, Bellman completeness, and/or hard margin (gap). In this work we propose value-based algorithms for offline RL with PAC guarantees under just partial coverage, specifically, coverage of just a single comparator policy, and realizability of soft (entropy-regularized) Q-function of the single policy and a related function defined as a saddle point of certain minimax optimization problem. This offers refined and generally more lax conditions for offline RL. We further show an analogous result for vanilla Q-functions under a soft margin condition. To attain these guarantees, we leverage novel minimax learning algorithms to accurately estimate soft or vanilla Q-functions with $L^2$-convergence guarantees. Our algorithms' loss functions arise from casting the estimation problems as nonlinear convex optimization problems and Lagrangifying.

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