On Limited-Memory Subsampling Strategies for Bandits

TL;DR

This paper demonstrates that a simple deterministic subsampling rule in bandit algorithms is asymptotically optimal, even with limited memory, and extends its applicability to non-stationary environments with changing reward distributions.

Contribution

It proves the asymptotic optimality of last-block subsampling with limited memory and introduces a variant suitable for non-stationary scenarios with abrupt changes.

Findings

Deterministic subsampling is asymptotically optimal in exponential families.

Limited memory does not compromise the optimality guarantees.

The proposed method performs well in non-stationary environments with abrupt changes.

Abstract

There has been a recent surge of interest in nonparametric bandit algorithms based on subsampling. One drawback however of these approaches is the additional complexity required by random subsampling and the storage of the full history of rewards. Our first contribution is to show that a simple deterministic subsampling rule, proposed in the recent work of Baudry et al. (2020) under the name of ''last-block subsampling'', is asymptotically optimal in one-parameter exponential families. In addition, we prove that these guarantees also hold when limiting the algorithm memory to a polylogarithmic function of the time horizon. These findings open up new perspectives, in particular for non-stationary scenarios in which the arm distributions evolve over time. We propose a variant of the algorithm in which only the most recent observations are used for subsampling, achieving optimal regret guarantees under the assumption of a known number of abrupt changes. Extensive numerical simulations highlight the merits of this approach, particularly when the changes are not only affecting the means of the rewards.