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Is Local SGD Better than Minibatch SGD?

Blake Woodworth · Kumar Kshitij Patel · Sebastian Stich · Zhen Dai · Brian Bullins · Brendan McMahan · Ohad Shamir · Nati Srebro

Keywords: [ Convex Optimization ] [ Parallel and Distributed Learning ] [ Optimization - Large Scale, Parallel and Distributed ]


We study local SGD (also known as parallel SGD and federated SGD), a natural and frequently used distributed optimization method. Its theoretical foundations are currently lacking and we highlight how all existing error guarantees in the convex setting are dominated by a simple baseline, minibatch SGD. (1) For quadratic objectives we prove that local SGD strictly dominates minibatch SGD and that accelerated local SGD is minmax optimal for quadratics; (2) For general convex objectives we provide the first guarantee that at least \emph{sometimes} improves over minibatch SGD, but our guarantee does not always improve over, nor even match, minibatch SGD; (3) We show that indeed local SGD does \emph{not} dominate minibatch SGD by presenting a lower bound on the performance of local SGD that is worse than the minibatch SGD guarantee.

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