A New Algorithm for Non-stationary Contextual Bandits: Efficient, Optimal, and Parameter-free

TL;DR

This paper introduces a parameter-free, efficient, and optimal algorithm for non-stationary contextual bandits that adapts to unknown data shifts and achieves improved dynamic regret bounds.

Contribution

The authors develop the first adaptive, parameter-free algorithm for non-stationary contextual bandits with improved regret bounds and practical implementation via an ERM oracle.

Findings

Achieves dynamic regret of O(min{√ST, Δ^{1/3} T^{2/3}}).

Introduces replay phases to detect non-stationarity.

Outperforms previous bounds in related work.

Abstract

We propose the first contextual bandit algorithm that is parameter-free, efficient, and optimal in terms of dynamic regret. Specifically, our algorithm achieves dynamic regret $\mathcal{O}(\min\{\sqrt{ST}, \Delta^{\frac{1}{3}}T^{\frac{2}{3}}\})$ for a contextual bandit problem with $T$ rounds, $S$ switches and $\Delta$ total variation in data distributions. Importantly, our algorithm is adaptive and does not need to know $S$ or $\Delta$ ahead of time, and can be implemented efficiently assuming access to an ERM oracle. Our results strictly improve the $\mathcal{O}(\min \{S^{\frac{1}{4}}T^{\frac{3}{4}}, \Delta^{\frac{1}{5}}T^{\frac{4}{5}}\})$ bound of (Luo et al., 2018), and greatly generalize and improve the $\mathcal{O}(\sqrt{ST})$ result of (Auer et al, 2018) that holds only for the two-armed bandit problem without contextual information. The key novelty of our algorithm is to introduce replay phases, in which the algorithm acts according to its previous decisions for a certain amount of time in order to detect non-stationarity while maintaining a good balance between exploration and exploitation.