A Survey of Risk-Aware Multi-Armed Bandits

TL;DR

This survey reviews risk-aware multi-armed bandit algorithms, discussing risk measures, concentration inequalities, and problem settings, highlighting challenges and future directions in risk-sensitive decision-making.

Contribution

It consolidates existing research on risk measures in multi-armed bandits, analyzing algorithms for regret minimization and best-arm identification under risk considerations.

Findings

Overview of various risk measures and their properties

Analysis of concentration inequalities for risk measures

Discussion of challenges and future research directions

Abstract

In several applications such as clinical trials and financial portfolio optimization, the expected value (or the average reward) does not satisfactorily capture the merits of a drug or a portfolio. In such applications, risk plays a crucial role, and a risk-aware performance measure is preferable, so as to capture losses in the case of adverse events. This survey aims to consolidate and summarise the existing research on risk measures, specifically in the context of multi-armed bandits. We review various risk measures of interest, and comment on their properties. Next, we review existing concentration inequalities for various risk measures. Then, we proceed to defining risk-aware bandit problems, We consider algorithms for the regret minimization setting, where the exploration-exploitation trade-off manifests, as well as the best-arm identification setting, which is a pure exploration problem -- both in the context of risk-sensitive measures. We conclude by commenting on persisting challenges and fertile areas for future research.