A Novel Confidence-Based Algorithm for Structured Bandits

TL;DR

This paper introduces a confidence-based phased algorithm for structured stochastic bandits that leverages arm correlations to reduce suboptimal arm pulls and achieve bounded regret in certain structures.

Contribution

It presents a new algorithm exploiting reward structure to improve arm selection efficiency and provides theoretical bounds and empirical validation.

Findings

Reduces the number of suboptimal arm pulls in structured bandits.

Achieves constant regret in certain structured bandit problems.

Demonstrates superior performance over existing methods in numerical experiments.

Abstract

We study finite-armed stochastic bandits where the rewards of each arm might be correlated to those of other arms. We introduce a novel phased algorithm that exploits the given structure to build confidence sets over the parameters of the true bandit problem and rapidly discard all sub-optimal arms. In particular, unlike standard bandit algorithms with no structure, we show that the number of times a suboptimal arm is selected may actually be reduced thanks to the information collected by pulling other arms. Furthermore, we show that, in some structures, the regret of an anytime extension of our algorithm is uniformly bounded over time. For these constant-regret structures, we also derive a matching lower bound. Finally, we demonstrate numerically that our approach better exploits certain structures than existing methods.