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

• URL: http://arxiv.org/abs/2503.08896v1
• Date: Tue, 11 Mar 2025 21:18:54 GMT
• Title: Risk-sensitive Bandits: Arm Mixture Optimality and Regret-efficient Algorithms
• Authors: Meltem Tatlı, Arpan Mukherjee, Prashanth L. A., Karthikeyan Shanmugam, Ali Tajer,
• Abstract summary: 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.<n>An important and hitherto unknown observation is that for a wide range of riskmetrics, the optimal bandit policy involves selecting a mixture of arms.
• Score: 34.876652087068734
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $O((\log T/T )^{\nu})$, where $T$ is the horizon, and $\nu>0$ is a riskmetric-specific constant.

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