Distributed Online Learning for Joint Regret with Communication Constraints
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In this paper we consider a distributed online learning setting for joint regret with communication constraints. This is a multi-agent setting in which in each round t an adversary activates an agent, which has to issue a prediction. A subset of all the agents may then communicate a b-bit message to their neighbors in a graph. All agents cooperate to control the joint regret, which is the sum of the losses of the agents minus the losses evaluated at the best fixed common comparator parameters u. We provide a comparator-adaptive algorithm for this setting, which means that the joint regret scales with the norm of the comparator u. To address communication constraints we provide deterministic and stochastic gradient compression schemes and show that with these compression schemes our algorithm has worst-case optimal regret for the case that all agents communicate in every round. Additionally, we exploit the comparator-adaptive property of our algorithm to learn the best partition from a set of candidate partitions, which allows different subsets of agents to learn a different comparator.
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