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

• URL: http://arxiv.org/abs/2304.07504v2
• Date: Mon, 30 Oct 2023 14:18:37 GMT
• Title: Stochastic Distributed Optimization under Average Second-order Similarity: Algorithms and Analysis
• Authors: Dachao Lin, Yuze Han, Haishan Ye, Zhihua Zhang
• Abstract summary: We study finite-sum distributed optimization problems involving a master node and $n-1$ local nodes. We propose two new algorithms, SVRS and AccSVRS, motivated by previous works.
• Score: 36.646876613637325
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study finite-sum distributed optimization problems involving a master node and $n-1$ local nodes under the popular $\delta$-similarity and $\mu$-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 $\tilde{\mathcal{O}}(n {+} \sqrt{n}\delta/\mu)$ compared to existing non-accelerated algorithms. Applying the framework proposed in Katyusha X, we also develop a directly accelerated version named AccSVRS with the $\tilde{\mathcal{O}}(n {+} n^{3/4}\sqrt{\delta/\mu})$ 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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