A minimax learning approach to off-policy evaluation in confounded Partially Observable Markov Decision Processes

Shi, Chengchun ORCID: 0000-0001-7773-2099, Uehara, Masatoshi, Uehara, Masatoshi, Huang, Jiawei and Jiang, Nan (2022) A minimax learning approach to off-policy evaluation in confounded Partially Observable Markov Decision Processes. Proceedings of Machine Learning Research. ISSN 2640-3498

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Abstract

We consider off-policy evaluation (OPE) in Partially Observable Markov Decision Processes (POMDPs), where the evaluation policy depends only on observable variables and the behavior policy depends on unobservable latent variables. Existing works either assume no unmeasured confounders, or focus on settings where both the observation and the state spaces are tabular. In this work, we first propose novel identification methods for OPE in POMDPs with latent confounders, by introducing bridge functions that link the target policy’s value and the observed data distribution. We next propose minimax estimation methods for learning these bridge functions, and construct three estimators based on these estimated bridge functions, corresponding to a value function-based estimator, a marginalized importance sampling estimator, and a doubly-robust estimator. Our proposal permits general function approximation and is thus applicable to settings with continuous or large observation/state spaces. The nonasymptotic and asymptotic properties of the proposed estimators are investigated in detail.

Item Type:	Article
Additional Information:	© 2022 The Author(s)
Divisions:	Statistics
Date Deposited:	16 May 2022 10:42
Last Modified:	20 Dec 2024 00:57
URI:	http://eprints.lse.ac.uk/id/eprint/115104

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