Off-Policy Evaluation for Episodic Partially Observable Markov Decision Processes under Non-Parametric Models

TL;DR

This paper introduces a non-parametric approach for off-policy evaluation in episodic POMDPs with continuous states, utilizing V-bridge functions and time-dependent proxies, and provides the first finite-sample error bounds for this setting.

Contribution

It develops a novel non-parametric identification method and recursive algorithm for OPE in POMDPs, with finite-sample error bounds, under non-parametric models.

Findings

Established finite-sample error bounds for V-bridge function estimation.

Demonstrated the effectiveness of the recursive fitted-Q-evaluation algorithm.

Provided theoretical guarantees for policy value estimation in complex POMDPs.

Abstract

We study the problem of off-policy evaluation (OPE) for episodic Partially Observable Markov Decision Processes (POMDPs) with continuous states. Motivated by the recently proposed proximal causal inference framework, we develop a non-parametric identification result for estimating the policy value via a sequence of so-called V-bridge functions with the help of time-dependent proxy variables. We then develop a fitted-Q-evaluation-type algorithm to estimate V-bridge functions recursively, where a non-parametric instrumental variable (NPIV) problem is solved at each step. By analyzing this challenging sequential NPIV problem, we establish the finite-sample error bounds for estimating the V-bridge functions and accordingly that for evaluating the policy value, in terms of the sample size, length of horizon and so-called (local) measure of ill-posedness at each step. To the best of our knowledge, this is the first finite-sample error bound for OPE in POMDPs under non-parametric models.