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. A Python implementation of our proposal is available at https://github.com/jiaweihhuang/ Confounded-POMDP-Exp.
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Proximal Reinforcement Learning: Efficient Off-Policy Evaluation in Partially Observed Markov Decision Processes
In applications of offline reinforcement learning to observational data, such as in healthcare or education, a general concern is that observed actions might be affected by unobserved factors, inducing confounding and biasing estimates derived assuming a perfect Markov decision process (MDP) model. In “Proximal Reinforcement Learning: Efficient Off-Policy Evaluation in Partially Observed Markov Decision Processes,” A. Bennett and N. Kallus tackle this by considering off-policy evaluation in a partially observed MDP (POMDP). Specifically, they consider estimating the value of a given target policy in an unknown POMDP, given observations of trajectories generated by a different and unknown policy, which may depend on the unobserved states. They consider both when the target policy value can be identified the observed data and, given identification, how best to estimate it. Both these problems are addressed by extending the framework of proximal causal inference to POMDP settings, using sequences of so-called bridge functions. This results in a novel framework for off-policy evaluation in POMDPs that they term proximal reinforcement learning, which they validate in various empirical settings.
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- Award ID(s):
- 1939704
- PAR ID:
- 10466992
- Publisher / Repository:
- INFORMS
- Date Published:
- Journal Name:
- Operations Research
- ISSN:
- 0030-364X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1287/opre.2021.0781
