Minimax Weight and Q-Function Learning for Off-Policy Evaluation

TL;DR

This paper introduces new estimators MWL and MQL for off-policy evaluation in reinforcement learning, which estimate importance ratios and value functions directly, improving robustness and theoretical understanding.

Contribution

The paper proposes two novel estimators, MWL and MQL, that enhance off-policy evaluation by removing reliance on known behavior policies and providing a unified theoretical framework.

Findings

MWL directly estimates importance ratios without behavior policy knowledge

MQL minimizes Bellman errors and can be combined with MWL for robustness

Sample complexity analyses show asymptotic optimality in tabular settings

Abstract

We provide theoretical investigations into off-policy evaluation in reinforcement learning using function approximators for (marginalized) importance weights and value functions. Our contributions include: (1) A new estimator, MWL, that directly estimates importance ratios over the state-action distributions, removing the reliance on knowledge of the behavior policy as in prior work (Liu et al., 2018). (2) Another new estimator, MQL, obtained by swapping the roles of importance weights and value-functions in MWL. MQL has an intuitive interpretation of minimizing average Bellman errors and can be combined with MWL in a doubly robust manner. (3) Several additional results that offer further insights into these methods, including the sample complexity analyses of MWL and MQL, their asymptotic optimality in the tabular setting, how the learned importance weights depend the choice of the discriminator class, and how our methods provide a unified view of some old and new algorithms in RL.