Non-Stationary Lipschitz Bandits

Nicolas Nguyen, Solenne Gaucher, Claire Vernade

Keywords: non-stationary bandits, Lipschitz bandits, tracking most significant shifts

TL;DR: We study the problem of non-stationary Lipschitz bandits and achieve minimax optimal rate without knowledge of the non-stationarity.

Abstract:

We study the problem of non-stationary Lipschitz bandits, where the number of actions is infinite and the reward function, satisfying a Lipschitz assumption, can change arbitrarily over time. We design an algorithm that adaptively tracks the recently introduced notion of significant shifts, defined by large deviations of the cumulative reward function. To detect such reward changes, our algorithm leverages a hierarchical discretization of the action space. Without requiring any prior knowledge of the non-stationarity, our algorithm
achieves a minimax-optimal dynamic regret bound of $\mathcal{\widetilde{O}}(\tilde{L}^{1/3}T^{2/3})$, where $\tilde{L}$ is the number of significant shifts and $T$ the horizon. This result provides the first optimal guarantee in this setting.

Primary Area: Theory (e.g., control theory, learning theory, algorithmic game theory)

Submission Number: 1681