Doubly Robust Off-Policy Value and Gradient Estimation for Deterministic Policies

TL;DR

This paper introduces new doubly robust estimators for off-policy evaluation and policy gradient estimation in offline reinforcement learning with deterministic policies and continuous actions, addressing the challenge of non-existent density ratios.

Contribution

It proposes kernel-based doubly robust estimators for deterministic policies in continuous action spaces, with theoretical analysis of their asymptotic mean-squared error.

Findings

New estimators handle deterministic policies where density ratios do not exist.

Asymptotic analysis shows error bounds independent of horizon length.

Proposed methods outperform existing approaches in relevant settings.

Abstract

Offline reinforcement learning, wherein one uses off-policy data logged by a fixed behavior policy to evaluate and learn new policies, is crucial in applications where experimentation is limited such as medicine. We study the estimation of policy value and gradient of a deterministic policy from off-policy data when actions are continuous. Targeting deterministic policies, for which action is a deterministic function of state, is crucial since optimal policies are always deterministic (up to ties). In this setting, standard importance sampling and doubly robust estimators for policy value and gradient fail because the density ratio does not exist. To circumvent this issue, we propose several new doubly robust estimators based on different kernelization approaches. We analyze the asymptotic mean-squared error of each of these under mild rate conditions for nuisance estimators. Specifically, we demonstrate how to obtain a rate that is independent of the horizon length.