Variance-Aware Off-Policy Evaluation with Linear Function Approximation

• URL: http://arxiv.org/abs/2106.11960v1
• Date: Tue, 22 Jun 2021 17:58:46 GMT
• Title: Variance-Aware Off-Policy Evaluation with Linear Function Approximation
• Authors: Yifei Min and Tianhao Wang and Dongruo Zhou and Quanquan Gu
• Abstract summary: We study the off-policy evaluation problem in reinforcement learning with linear function approximation. We propose an algorithm, VA-OPE, which uses the estimated variance of the value function to reweight the Bellman residual in Fitted Q-Iteration.
• Score: 85.75516599931632
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the off-policy evaluation (OPE) problem in reinforcement learning with linear function approximation, which aims to estimate the value function of a target policy based on the offline data collected by a behavior policy. We propose to incorporate the variance information of the value function to improve the sample efficiency of OPE. More specifically, for time-inhomogeneous episodic linear Markov decision processes (MDPs), we propose an algorithm, VA-OPE, which uses the estimated variance of the value function to reweight the Bellman residual in Fitted Q-Iteration. We show that our algorithm achieves a tighter error bound than the best-known result. We also provide a fine-grained characterization of the distribution shift between the behavior policy and the target policy. Extensive numerical experiments corroborate our theory.

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