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

• URL: http://arxiv.org/abs/2209.10064v1
• Date: Wed, 21 Sep 2022 01:44:45 GMT
• Title: Off-Policy Evaluation for Episodic Partially Observable Markov Decision Processes under Non-Parametric Models
• Authors: Rui Miao, Zhengling Qi, Xiaoke Zhang
• Abstract summary: 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 causal inference framework, we develop a non-parametric identification result for estimating the policy value. This is the first finite-sample error bound for OPE in POMDPs under non-parametric models.
• Score: 2.3411358616430435
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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