Batched Multi-armed Bandits Problem
This addresses an open problem in sequential decision-making for scenarios with limited data batches, providing theoretical guarantees for multi-armed bandits.
The paper tackles the batched multi-armed bandit problem by proposing the BaSE policy, which achieves rate-optimal regrets within logarithmic factors for multi-armed cases, with matching lower bounds even for adaptive batch sizes.
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.