A Change-Detection Based Thompson Sampling Framework for Non-Stationary Bandits

TL;DR

This paper introduces TS-CD, a change-detection based Thompson sampling algorithm for non-stationary bandit problems, which effectively detects environment changes and outperforms existing strategies in wireless network applications.

Contribution

The paper proposes a novel TS-based algorithm with change detection for non-stationary bandits, providing theoretical bounds and demonstrating superior performance in wireless network scenarios.

Findings

TS-CD detects changes effectively in non-stationary environments.

TS-CD achieves asymptotic regret optimality under certain conditions.

TS-CD outperforms classical and other adaptive bandit algorithms in wireless network tests.

Abstract

We consider a non-stationary two-armed bandit framework and propose a change-detection based Thompson sampling (TS) algorithm, named TS with change-detection (TS-CD), to keep track of the dynamic environment. The non-stationarity is modeled using a Poisson arrival process, which changes the mean of the rewards on each arrival. The proposed strategy compares the empirical mean of the recent rewards of an arm with the estimate of the mean of the rewards from its history. It detects a change when the empirical mean deviates from the mean estimate by a value larger than a threshold. Then, we characterize the lower bound on the duration of the time-window for which the bandit framework must remain stationary for TS-CD to successfully detect a change when it occurs. Consequently, our results highlight an upper bound on the parameter for the Poisson arrival process, for which the TS-CD achieves asymptotic regret optimality with high probability. Finally, we validate the efficacy of TS-CD by testing it for edge-control of radio access technique (RAT)-selection in a wireless network. Our results show that TS-CD not only outperforms the classical max-power RAT selection strategy but also other actively adaptive and passively adaptive bandit algorithms that are designed for non-stationary environments.