Nearly Optimal Adaptive Procedure with Change Detection for Piecewise-Stationary Bandit

Abstract

Multi-armed bandit (MAB) is a class of online learning problems where a learning agent aims to maximize its expected cumulative reward while repeatedly selecting to pull arms with unknown reward distributions. We consider a scenario where the reward distributions may change in a piecewise-stationary fashion at unknown time steps. We show that by incorporating a simple change-detection component with classic UCB algorithms to detect and adapt to changes, our so-called M-UCB algorithm can achieve nearly optimal regret bound on the order of O(MKT T), where T is the number of time steps, K is the number of arms, and M is the number of stationary segments. Comparison with the best available lower bound shows that our M-UCB is nearly optimal in T up to a logarithmic factor. We also compare M-UCB with the state-of-the-art algorithms in numerical experiments using a public Yahoo! dataset to demonstrate its superior performance.

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Reproductions