Best-Arm Identification with Noisy Actuation

2026-04-02

AI Summary

This work addresses the problem of distributed best-arm identification in multi-armed bandits, where a central learner communicates instructions to agents over a noisy discrete memoryless channel, introducing communication uncertainty. For the first time, the study establishes a theoretical connection between this setting and the zero-error capacity of the communication channel. The authors propose a joint communication-and-decision-making strategy that adapts to varying agent capabilities. Leveraging information-theoretic analysis, the designed algorithm achieves efficient and robust best-arm identification while guaranteeing theoretical reliability under channel noise constraints.

Abstract

In this paper, we consider a multi-armed bandit (MAB) instance and study how to identify the best arm when arm commands are conveyed from a central learner to a distributed agent over a discrete memoryless channel (DMC). Depending on the agent capabilities, we provide communication schemes along with their analysis, which interestingly relate to the zero-error capacity of the underlying DMC.

Problem

• Best-Arm Identification
• Noisy Actuation
• Multi-Armed Bandit
• Discrete Memoryless Channel
• Zero-Error Capacity

Innovation

• Best-arm identification
• Noisy actuation
• Discrete memoryless channel
• Zero-error capacity
• Multi-armed bandit