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A continuous-time analysis of distributed stochastic gradient
We analyze the effect of synchronization on distributed stochastic gradient
algorithms. By exploiting an analogy with dynamical models of biological quorum
sensing -- where synchronization between agents is induced through
communication with a common signal -- we quantify how synchronization can
significantly reduce the magnitude of the noise felt by the individual
distributed agents and by their spatial mean. This noise reduction is in turn
associated with a reduction in the smoothing of the loss function imposed by
the stochastic gradient approximation. Through simulations on model non-convex
objectives, we demonstrate that coupling can stabilize higher noise levels and
improve convergence. We provide a convergence analysis for strongly convex
functions by deriving a bound on the expected deviation of the spatial mean of
the agents from the global minimizer for an algorithm based on quorum sensing,
the same algorithm with momentum, and the Elastic Averaging SGD (EASGD)
algorithm. We discuss extensions to new algorithms which allow each agent to
broadcast its current measure of success and shape the collective computation
accordingly. We supplement our theoretical analysis with numerical experiments
on convolutional neural networks trained on the CIFAR-10 dataset, where we note
a surprising regularizing property of EASGD even when applied to the
non-distributed case. This observation suggests alternative second-order
in-time algorithms for non-distributed optimization that are competitive with
momentum methods.Comment: 9/14/19 : Final version, accepted for publication in Neural
Computation. 4/7/19 : Significant edits: addition of simulations, deep
network results, and revisions throughout. 12/28/18: Initial submissio
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