Risk-sensitive Bandits: Arm Mixture Optimality and Regret-efficient Algorithms

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Tatlı, Meltem, Mukherjee, Arpan, A., Prashanth L., Shanmugam, Karthikeyan, Tajer, Ali
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866912270201651200
author Tatlı, Meltem
Mukherjee, Arpan
A., Prashanth L.
Shanmugam, Karthikeyan
Tajer, Ali
author_facet Tatlı, Meltem
Mukherjee, Arpan
A., Prashanth L.
Shanmugam, Karthikeyan
Tajer, Ali
contents This paper introduces a general framework for risk-sensitive bandits that integrates the notions of risk-sensitive objectives by adopting a rich class of distortion riskmetrics. The introduced framework subsumes the various existing risk-sensitive models. An important and hitherto unknown observation is that for a wide range of riskmetrics, the optimal bandit policy involves selecting a mixture of arms. This is in sharp contrast to the convention in the multi-arm bandit algorithms that there is generally a solitary arm that maximizes the utility, whether purely reward-centric or risk-sensitive. This creates a major departure from the principles for designing bandit algorithms since there are uncountable mixture possibilities. The contributions of the paper are as follows: (i) it formalizes a general framework for risk-sensitive bandits, (ii) identifies standard risk-sensitive bandit models for which solitary arm selections is not optimal, (iii) and designs regret-efficient algorithms whose sampling strategies can accurately track optimal arm mixtures (when mixture is optimal) or the solitary arms (when solitary is optimal). The algorithms are shown to achieve a regret that scales according to $O((\log T/T )^ν)$, where $T$ is the horizon, and $ν>0$ is a riskmetric-specific constant.
format Preprint
id arxiv_https___arxiv_org_abs_2503_08896
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Risk-sensitive Bandits: Arm Mixture Optimality and Regret-efficient Algorithms
Tatlı, Meltem
Mukherjee, Arpan
A., Prashanth L.
Shanmugam, Karthikeyan
Tajer, Ali
Machine Learning
This paper introduces a general framework for risk-sensitive bandits that integrates the notions of risk-sensitive objectives by adopting a rich class of distortion riskmetrics. The introduced framework subsumes the various existing risk-sensitive models. An important and hitherto unknown observation is that for a wide range of riskmetrics, the optimal bandit policy involves selecting a mixture of arms. This is in sharp contrast to the convention in the multi-arm bandit algorithms that there is generally a solitary arm that maximizes the utility, whether purely reward-centric or risk-sensitive. This creates a major departure from the principles for designing bandit algorithms since there are uncountable mixture possibilities. The contributions of the paper are as follows: (i) it formalizes a general framework for risk-sensitive bandits, (ii) identifies standard risk-sensitive bandit models for which solitary arm selections is not optimal, (iii) and designs regret-efficient algorithms whose sampling strategies can accurately track optimal arm mixtures (when mixture is optimal) or the solitary arms (when solitary is optimal). The algorithms are shown to achieve a regret that scales according to $O((\log T/T )^ν)$, where $T$ is the horizon, and $ν>0$ is a riskmetric-specific constant.
title Risk-sensitive Bandits: Arm Mixture Optimality and Regret-efficient Algorithms
topic Machine Learning
url https://arxiv.org/abs/2503.08896