A Minimax Learning Approach to Off-Policy Evaluation in Confounded Partially Observable Markov Decision Processes
This addresses the problem of evaluating policies in complex, confounded environments for reinforcement learning practitioners, representing an incremental advance by extending prior work to more general settings.
The authors tackled off-policy evaluation in partially observable Markov decision processes with latent confounders, proposing novel identification and minimax estimation methods that enable general function approximation and yield three estimators with analyzed properties.
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.