Bounded Regret for Finite-Armed Structured Bandits

TL;DR

This paper introduces a new algorithm for structured bandit problems where arm rewards are interdependent, achieving finite regret under certain conditions and nearly optimal performance in some cases.

Contribution

The paper proposes a novel algorithm for structured bandits with interdependent arms and establishes finite regret bounds and near-optimality in specific scenarios.

Findings

The algorithm achieves finite expected cumulative regret in certain structured bandit problems.

Lower bounds show the near-optimality of the proposed algorithm in some cases.

The approach extends traditional bandit analysis to interdependent reward settings.

Abstract

We study a new type of K-armed bandit problem where the expected return of one arm may depend on the returns of other arms. We present a new algorithm for this general class of problems and show that under certain circumstances it is possible to achieve finite expected cumulative regret. We also give problem-dependent lower bounds on the cumulative regret showing that at least in special cases the new algorithm is nearly optimal.