Communication-efficient SGD: From Local SGD to One-Shot Averaging

Abstract

We consider speeding up stochastic gradient descent (SGD) by parallelizing it across multiple workers. We assume the same data set is shared among N workers, who can take SGD steps and coordinate with a central server. While it is possible to obtain a linear reduction in the variance by averaging all the stochastic gradient at every step, this requires a lot of communication between the workers and the server, which can dramatically reduce the gains from parallelism. The Local SGD method, proposed and analyzed in the earlier literature, suggests machines should make many local steps between such communications. While the initial analysis of Local SGD showed it needs Ω( √ T ) communications for T local gradient steps in order for the error to scale proportionately to 1/(N T ), this has been successively improved in a string of papers, with the state-of-the-art requiring Ω (N ( polynomial in log (T ))) communications. In this paper, we suggest a Local SGD scheme that communicates less overall by communicating less frequently as the number of iterations grows. Our analysis shows that this can achieve an error that scales as 1/(N T ) with a number of communications that is completely independent of T . In particular, we show that Ω(N ) communications are sufficient. Empirical evidence suggests this bound is close to tight as we further show that √ N or N 3/4 communications fail to achieve linear speed-up in simulations. Moreover, we show that under mild assumptions, the main of which is twice differentiability on any neighborhood of the optimal solution, one-shot averaging which only uses a single round of communication can also achieve the optimal convergence rate asymptotically.Preprint. Under review.

Fast Composite Optimization and Statistical Recovery in Federated Learning

“…However, their analysis and algorithm are not applicable in the composite setting, and they do not consider statistical recovery at all. A more recent work Spiridonoff et al (2021) showed that the number of rounds can be independent of T under homogeneous setting. Recently, there is a line of work focusing on analyzing nonconvex problems in FL (Yu et al, 2019b;a;Basu et al, 2019;Haddadpour et al, 2019).…”