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

Understand

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.