Regret Analysis for Hierarchical Experts Bandit Problem

TL;DR

This paper extends the multi-armed bandit problem to a hierarchical expert setting, analyzing regret growth and proposing bounds for UCB strategies, with experiments illustrating practical implications.

Contribution

It introduces a hierarchical bandit model, analyzes regret growth across layers, and provides sub-linear bounds for hierarchical UCB strategies with experimental validation.

Findings

Regret grows linearly with the number of layers in the worst case.

Hierarchical UCB strategies can achieve sub-linear regret bounds.

Experiments demonstrate the practical relevance of the theoretical results.

Abstract

We study an extension of standard bandit problem in which there are R layers of experts. Multi-layered experts make selections layer by layer and only the experts in the last layer can play arms. The goal of the learning policy is to minimize the total regret in this hierarchical experts setting. We first analyze the case that total regret grows linearly with the number of layers. Then we focus on the case that all experts are playing Upper Confidence Bound (UCB) strategy and give several sub-linear upper bounds for different circumstances. Finally, we design some experiments to help the regret analysis for the general case of hierarchical UCB structure and show the practical significance of our theoretical results. This article gives many insights about reasonable hierarchical decision structure.