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

Machine Learning;Distributed, Parallel, and Cluster Computing;Multiagent Systems