Instance-Dependent Confidence and Early Stopping for Reinforcement Learning

• URL: http://arxiv.org/abs/2201.08536v1
• Date: Fri, 21 Jan 2022 04:25:35 GMT
• Title: Instance-Dependent Confidence and Early Stopping for Reinforcement Learning
• Authors: Koulik Khamaru, Eric Xia, Martin J. Wainwright, Michael I. Jordan
• Abstract summary: Various algorithms for reinforcement learning (RL) exhibit dramatic variation in their convergence rates as a function of problem structure. This research provides guarantees that explain textitex post the performance differences observed. A natural next step is to convert these theoretical guarantees into guidelines that are useful in practice.
• Score: 99.57168572237421
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Various algorithms for reinforcement learning (RL) exhibit dramatic variation in their convergence rates as a function of problem structure. Such problem-dependent behavior is not captured by worst-case analyses and has accordingly inspired a growing effort in obtaining instance-dependent guarantees and deriving instance-optimal algorithms for RL problems. This research has been carried out, however, primarily within the confines of theory, providing guarantees that explain \textit{ex post} the performance differences observed. A natural next step is to convert these theoretical guarantees into guidelines that are useful in practice. We address the problem of obtaining sharp instance-dependent confidence regions for the policy evaluation problem and the optimal value estimation problem of an MDP, given access to an instance-optimal algorithm. As a consequence, we propose a data-dependent stopping rule for instance-optimal algorithms. The proposed stopping rule adapts to the instance-specific difficulty of the problem and allows for early termination for problems with favorable structure.

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