Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems

TL;DR

This paper reviews regret analysis in multi-armed bandit problems, focusing on stochastic and adversarial payoff models, and discusses various extensions like contextual bandits, highlighting their theoretical properties and applications.

Contribution

It provides a comprehensive survey of regret analysis techniques for both stochastic and adversarial bandit models, including key variants and extensions.

Findings

Regret bounds are well-understood for i.i.d. payoffs.

Adversarial bandit models require different algorithms with regret guarantees.

Extensions like contextual bandits expand the applicability of bandit frameworks.

Abstract

Multi-armed bandit problems are the most basic examples of sequential decision problems with an exploration-exploitation trade-off. This is the balance between staying with the option that gave highest payoffs in the past and exploring new options that might give higher payoffs in the future. Although the study of bandit problems dates back to the Thirties, exploration-exploitation trade-offs arise in several modern applications, such as ad placement, website optimization, and packet routing. Mathematically, a multi-armed bandit is defined by the payoff process associated with each option. In this survey, we focus on two extreme cases in which the analysis of regret is particularly simple and elegant: i.i.d. payoffs and adversarial payoffs. Besides the basic setting of finitely many actions, we also analyze some of the most important variants and extensions, such as the contextual bandit model.