A Change-Detection Based Thompson Sampling Framework for Non-Stationary Bandits
This addresses the challenge of adapting to changing reward distributions in bandit problems, which is incremental as it builds on Thompson sampling with change-detection for specific non-stationary models.
The paper tackles the problem of non-stationary bandits by proposing a change-detection based Thompson sampling algorithm (TS-CD) to track dynamic environments, showing it achieves asymptotic regret optimality with high probability and outperforms existing bandit algorithms in a wireless network application.
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.