Projection Algorithms for Distributed Stochastic Optimization

Abstract

AbstractThis chapter focuses on introducing and solving the problem of composite constrained convex optimization with a sum of smooth convex functions and non-smooth regularization terms (ℓ1 norm) subject to locally general constraints. Each of the smooth objective functions is further thought of as the average of several constituent functions, which is motivated by the modern large-scale information processing problems in machine learning (the samples of a training dataset are randomly distributed across multiple computing nodes). We present a novel computation-efficient distributed stochastic gradient algorithm that makes use of both the variance-reduction methodology and the distributed stochastic gradient projection method with constant step-size to solve the problem in a distributed manner. Theoretical study shows that the suggested algorithm can discover the precise optimal solution in expectation when each constituent function (smooth) is strongly convex if the constant step-size is less than an explicitly calculated upper constraint. Regarding the current distributed methods, the suggested technique not only has a low computation cost in terms of the overall number of local gradient evaluations but is also suited for addressing general restricted optimization problems. Finally, the numerical proof is offered to show the suggested algorithm’s attractive performance.KeywordsComposite constrained optimizationDistributed stochastic algorithmComputation-efficientVariance reductionNon-smooth term