PREPRINT

# Doubly Inhomogeneous Reinforcement Learning

Liyuan Hu, Mengbing Li, Chengchun Shi, Zhenke Wu, Piotr Fryzlewicz

Submitted on 7 November 2022, last revised on 12 November 2022

## Abstract

This paper studies reinforcement learning (RL) in doubly inhomogeneous environments under temporal non-stationarity and subject heterogeneity. In a number of applications, it is commonplace to encounter datasets generated by system dynamics that may change over time and population, challenging high-quality sequential decision making. Nonetheless, most existing RL solutions require either temporal stationarity or subject homogeneity, which would result in sub-optimal policies if both assumptions were violated. To address both challenges simultaneously, we propose an original algorithm to determine the best data chunks" that display similar dynamics over time and across individuals for policy learning, which alternates between most recent change point detection and cluster identification. Our method is general, and works with a wide range of clustering and change point detection algorithms. It is multiply robust in the sense that it takes multiple initial estimators as input and only requires one of them to be consistent. Moreover, by borrowing information over time and population, it allows us to detect weaker signals and has better convergence properties when compared to applying the clustering algorithm per time or the change point detection algorithm per subject. Empirically, we demonstrate the usefulness of our method through extensive simulations and a real data application.

## Preprint

Subjects: Statistics - Machine Learning; Computer Science - Artificial Intelligence; Computer Science - Machine Learning