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Multi-Armed Bandit (MAB) systems are witnessing an upswing in applicationswithin multi-agent distributed environments, leading to the advancement ofcollaborative MAB algorithms. In such settings, communication between agentsexecuting actions and the primary learner making decisions can hinder thelearning process. A prevalent challenge in distributed learning is actionerasure, often induced by communication delays and/or channel noise. Thisresults in agents possibly not receiving the intended action from the learner,subsequently leading to misguided feedback. In this paper, we introduce novelalgorithms that enable learners to interact concurrently with distributedagents across heterogeneous action erasure channels with different actionerasure probabilities. We illustrate that, in contrast to existing banditalgorithms, which experience linear regret, our algorithms assure sub-linearregret guarantees. Our proposed solutions are founded on a meticulously craftedrepetition protocol and scheduling of learning across heterogeneous channels.To our knowledge, these are the first algorithms capable of effectivelylearning through heterogeneous action erasure channels. We substantiate thesuperior performance of our algorithm through numerical experiments,emphasizing their practical significance in addressing issues related tocommunication constraints and delays in multi-agent environments.

Multi-Agent Bandit Learning through Heterogeneous Action Erasure Channels