Batched Multi-armed Bandits Problem

TL;DR

This paper introduces the BaSE policy for batched multi-armed bandits, achieving near-optimal regret bounds even with adaptive batch sizes, and explores how the number of arms affects regret.

Contribution

It proposes a new policy that attains rate-optimal regret bounds for batched multi-armed bandits, addressing open questions about the impact of arm count and adaptive batching.

Findings

BaSE policy achieves near-optimal regret bounds.

Matching lower bounds established for adaptive batch sizes.

Analysis of the effect of the number of arms on regret.

Abstract

In this paper, we study the multi-armed bandit problem in the batched setting where the employed policy must split data into a small number of batches. While the minimax regret for the two-armed stochastic bandits has been completely characterized in \cite{perchet2016batched}, the effect of the number of arms on the regret for the multi-armed case is still open. Moreover, the question whether adaptively chosen batch sizes will help to reduce the regret also remains underexplored. In this paper, we propose the BaSE (batched successive elimination) policy to achieve the rate-optimal regrets (within logarithmic factors) for batched multi-armed bandits, with matching lower bounds even if the batch sizes are determined in an adaptive manner.