  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.
