A maximum-entropy approach to off-policy evaluation in average-reward MDPs

TL;DR

This paper introduces a maximum-entropy method for off-policy evaluation in average-reward MDPs, providing finite-sample error bounds for ergodic linear cases and a new distribution estimation approach for more general settings.

Contribution

It presents the first finite-sample error bounds for off-policy evaluation in ergodic linear average-reward MDPs and proposes a maximum-entropy distribution estimation method for approximate linear dynamics.

Findings

Finite-sample error bounds for ergodic linear MDPs.

Effective distribution estimation in general settings.

Successful empirical validation across multiple environments.

Abstract

This work focuses on off-policy evaluation (OPE) with function approximation in infinite-horizon undiscounted Markov decision processes (MDPs). For MDPs that are ergodic and linear (i.e. where rewards and dynamics are linear in some known features), we provide the first finite-sample OPE error bound, extending existing results beyond the episodic and discounted cases. In a more general setting, when the feature dynamics are approximately linear and for arbitrary rewards, we propose a new approach for estimating stationary distributions with function approximation. We formulate this problem as finding the maximum-entropy distribution subject to matching feature expectations under empirical dynamics. We show that this results in an exponential-family distribution whose sufficient statistics are the features, paralleling maximum-entropy approaches in supervised learning. We demonstrate the effectiveness of the proposed OPE approaches in multiple environments.