Multiplier Bootstrap-based Exploration

TL;DR

This paper introduces Multiplier Bootstrap-based Exploration (MBE), a versatile exploration strategy for bandit problems that provides optimal regret bounds and adapts well across different reward models.

Contribution

The paper proposes MBE, a novel bootstrap-based exploration method applicable to any reward model that uses weighted loss minimization, with proven optimal regret bounds.

Findings

MBE achieves rate-optimal regret bounds in multi-armed bandits.

MBE demonstrates strong performance in simulations and real data.

MBE is applicable to a wide range of reward models.

Abstract

Despite the great interest in the bandit problem, designing efficient algorithms for complex models remains challenging, as there is typically no analytical way to quantify uncertainty. In this paper, we propose Multiplier Bootstrap-based Exploration (MBE), a novel exploration strategy that is applicable to any reward model amenable to weighted loss minimization. We prove both instance-dependent and instance-independent rate-optimal regret bounds for MBE in sub-Gaussian multi-armed bandits. With extensive simulation and real data experiments, we show the generality and adaptivity of MBE.