Nested bandits

TL;DR

This paper introduces the nested exponential weights (NEW) algorithm for hierarchical bandit problems, effectively reducing regret by layered exploration in environments with many similar alternatives.

Contribution

It proposes a novel layered exploration algorithm tailored for nested bandits, improving regret bounds in settings with hierarchical similarities.

Findings

NEW algorithm achieves tighter regret bounds

Efficiently handles large sets with hierarchical similarities

Prevents excessive exploration of irrelevant options

Abstract

In many online decision processes, the optimizing agent is called to choose between large numbers of alternatives with many inherent similarities; in turn, these similarities imply closely correlated losses that may confound standard discrete choice models and bandit algorithms. We study this question in the context of nested bandits, a class of adversarial multi-armed bandit problems where the learner seeks to minimize their regret in the presence of a large number of distinct alternatives with a hierarchy of embedded (non-combinatorial) similarities. In this setting, optimal algorithms based on the exponential weights blueprint (like Hedge, EXP3, and their variants) may incur significant regret because they tend to spend excessive amounts of time exploring irrelevant alternatives with similar, suboptimal costs. To account for this, we propose a nested exponential weights (NEW) algorithm that performs a layered exploration of the learner's set of alternatives based on a nested, step-by-step selection method. In so doing, we obtain a series of tight bounds for the learner's regret showing that online learning problems with a high degree of similarity between alternatives can be resolved efficiently, without a red bus / blue bus paradox occurring.