Optimal regret bounds O(δ^{-1/2}√T) for convex and O(δ^{-1} log T) for strongly convex losses are achieved in distributed online convex optimization under compressed communication.
C.3 Proof of Lemma B.8 We first give the bound of the compression error of each learner
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Distributed Online Convex Optimization with Compressed Communication: Optimal Regret and Applications
Optimal regret bounds O(δ^{-1/2}√T) for convex and O(δ^{-1} log T) for strongly convex losses are achieved in distributed online convex optimization under compressed communication.