Structured Difference-of-Q via Orthogonal Learning

TL;DR

This paper introduces a dynamic orthogonal learning method for estimating and optimizing the difference of Q-functions in offline reinforcement learning, improving convergence and consistency in decision-making tasks.

Contribution

It develops a generalized R-learner for Q-function differences, leveraging orthogonal estimation to enhance convergence and enable structured contrast estimation in offline RL.

Findings

Improved convergence rates with orthogonal estimation.

Proven consistency of policy optimization under a margin condition.

Method effectively leverages black-box nuisance estimators.

Abstract

Offline reinforcement learning is important in many settings with available observational data but the inability to deploy new policies online due to safety, cost, and other concerns. Many recent advances in causal inference and machine learning target estimation of causal contrast functions such as CATE, which is sufficient for optimizing decisions and can adapt to potentially smoother structure. We develop a dynamic generalization of the R-learner (Nie and Wager 2021, Lewis and Syrgkanis 2021) for estimating and optimizing the difference of $Q^\pi$-functions, $Q^\pi(s,1)-Q^\pi(s,0)$ (which can be used to optimize multiple-valued actions). We leverage orthogonal estimation to improve convergence rates in the presence of slower nuisance estimation rates and prove consistency of policy optimization under a margin condition. The method can leverage black-box nuisance estimators of the $Q$-function and behavior policy to target estimation of a more structured $Q$-function contrast.