Risk-Averse Best Arm Set Identification with Fixed Budget and Fixed Confidence

TL;DR

This paper introduces a new stochastic bandit problem focusing on identifying Pareto-optimal arms that balance reward and risk using the mean-variance criterion, with a unified framework for fixed-confidence and fixed-budget settings.

Contribution

It proposes a novel meta-algorithmic framework for risk-aware bandit optimization that handles both regimes and provides theoretical guarantees and empirical validation.

Findings

Outperforms existing methods in accuracy and sample efficiency

Effective in synthetic benchmarks for risk-aware decision-making

Provides theoretical guarantees on solution correctness

Abstract

Decision making under uncertain environments in the maximization of expected reward while minimizing its risk is one of the ubiquitous problems in many subjects. Here, we introduce a novel problem setting in stochastic bandit optimization that jointly addresses two critical aspects of decision-making: maximizing expected reward and minimizing associated uncertainty, quantified via the mean-variance(MV) criterion. Unlike traditional bandit formulations that focus solely on expected returns, our objective is to efficiently and accurately identify the Pareto-optimal set of arms that strikes the best trade-off between expected performance and risk. We propose a unified meta-algorithmic framework capable of operating under both fixed-confidence and fixed-budget regimes, achieved through adaptive design of confidence intervals tailored to each scenario using the same sample exploration strategy. We provide theoretical guarantees on the correctness of the returned solutions in both settings. To complement this theoretical analysis, we conduct extensive empirical evaluations across synthetic benchmarks, demonstrating that our approach outperforms existing methods in terms of both accuracy and sample efficiency, highlighting its broad applicability to risk-aware decision-making tasks in uncertain environments.