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We consider the problem of online stochastic optimization in a distributedsetting with $M$ clients connected through a central server. We develop adistributed online learning algorithm that achieves order-optimal cumulativeregret with low communication cost measured in the total number of bitstransmitted over the entire learning horizon. This is in contrast to existingstudies which focus on the offline measure of simple regret for learningefficiency. The holistic measure for communication cost also departs from theprevailing approach that \emph{separately} tackles the communication frequencyand the number of bits in each communication round.

A Communication-Efficient Adaptive Algorithm for Federated Learning under Cumulative Regret