Stochastic Distributed Optimization under Average Second-order Similarity: Algorithms and Analysis

Abstract

We study finite-sum distributed optimization problems involving a master node and n-1 local nodes under the popular -similarity and -strong convexity conditions. We propose two new algorithms, SVRS and AccSVRS, motivated by previous works. The non-accelerated SVRS method combines the techniques of gradient sliding and variance reduction and achieves a better communication complexity of O(n + n/) compared to existing non-accelerated algorithms. Applying the framework proposed in Katyusha X, we also develop a directly accelerated version named AccSVRS with the O(n + n^3/4/) communication complexity. In contrast to existing results, our complexity bounds are entirely smoothness-free and exhibit superiority in ill-conditioned cases. Furthermore, we establish a nearly matched lower bound to verify the tightness of our AccSVRS method.

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Reproductions