A Modularized Framework for Piecewise-Stationary Restless Bandits

Kuan-Ta Li, Chia-Chun Lin, Ping-Chun Hsieh, Yu-Chih Huang

Abstract:

We study the piecewise-stationary restless multi-armed bandit (PS-RMAB) problem, where each arm evolves as a Markov chain but \emph{mean rewards may change across unknown segments}. To address the resulting exploration--detection delay trade-off, we propose a modular framework that integrates arbitrary RMAB base algorithms with change detection and a novel diminishing exploration mechanism. This design enables flexible plug-and-play use of existing solvers and detectors, while efficiently adapting
to mean changes without prior knowledge of their number.

To evaluate performance, we introduce a refined regret notion that measures the \emph{excess regret due to exploration and detection}, benchmarked against an oracle that restarts the base algorithm at the true change points. Under this metric, we prove a regret bound of
$\tilde{O}(\sqrt{LMKT})$, where $L$ denotes the maximum mixing time of the Markov chains across all arms and segments, $M$ the number of segments, $K$ the number of arms, and $T$ the horizon. Simulations confirm that our framework achieves regret close to that of the segment oracle and consistently outperforms base solvers that do not incorporate any mechanism to handle environmental hanges.

Submission Number: 1560