Best-Arm Identification with Noisy Actuation

TL;DR

This paper investigates how to identify the best arm in a multi-armed bandit setting when commands are transmitted over noisy channels, linking communication schemes to the channel's zero-error capacity.

Contribution

It introduces communication schemes tailored for distributed bandit problems over noisy channels, analyzing their effectiveness based on the channel's zero-error capacity.

Findings

Communication schemes are developed for noisy channels in bandit problems.

The analysis relates the success of identification to the zero-error capacity of the channel.

The schemes adapt to agent capabilities and channel properties.

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.