Robust Fitted-Q-Evaluation and Iteration under Sequentially Exogenous Unobserved Confounders

Published: 27 Oct 2023, Last Modified: 22 Dec 2023RealML-2023EveryoneRevisionsBibTeX
Keywords: robust offline reinforcement learning,
TL;DR: valid robust bounds on value functions from biased data can still be used to warmstart online learning
Abstract: Offline reinforcement learning is important in domains such as medicine, economics, and e-commerce where online experimentation is costly, dangerous or unethical, and where the true model is unknown. We study robust policy evaluation and policy optimization in the presence of sequentially-exogenous unobserved confounders under a sensitivity model. We propose and analyze orthogonalized robust fitted-Q-iteration that uses closed-form solutions of the robust Bellman operator to derive a loss minimization problem for the robust Q function, and adds a bias-correction to quantile estimation. Our algorithm enjoys the computational ease of fitted-Q-iteration and statistical improvements (reduced dependence on quantile estimation error) from orthogonalization. We provide sample complexity bounds, insights, and show effectiveness both in simulations and on real-world longitudinal healthcare data of treating sepsis. In particular, our model of sequential unobserved confounders yields an online Markov decision process, rather than partially observed Markov decision process: we illustrate how this can enable warm-starting optimistic reinforcement learning algorithms with valid robust bounds from observational data.
Submission Number: 53