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This paper analyzes the problem of best-arm identification in multi-armed bandits when arm selections are communicated over a discrete memoryless channel (DMC). The authors derive communication schemes that leverage the zero-error capacity of the DMC to optimize the exploration-exploitation trade-off under noisy actuation. The analysis reveals a direct relationship between the achievable performance in best-arm identification and the communication channel's capacity, providing insights into the fundamental limits of learning with noisy actions.
Noisy communication channels fundamentally limit the performance of multi-armed bandit algorithms, but exploiting the zero-error capacity of the channel can surprisingly improve best-arm identification.
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.
