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Distributed Stochastic Optimization with Compression for non-strongly convex objectives

Computer Modeling in Engineering & Sciences 2024年第4期139卷 459-481页

作者： Xuanjie Li Yuedong Xu School of Information Science and Technology Fudan UniversityShanghaiChina

We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local *** nodes exchange optimization parameters through the wireless network,large-scale training models can create communication bottlenecks,resulting in slower training *** address this issue,CHOCO-SGD was proposed,which allows compressing information with arbitrary precision without reducing the convergence rate for strongly convex objective ***,most convex functions are not strongly convex(such as logistic regression or Lasso),which raises the question of whether this algorithm can be applied to non-strongly convex *** this paper,we provide the first theoretical analysis of the convergence rate of CHOCO-SGD on non-strongly convex *** derive a sufficient condition,which limits the fidelity of compression,to guarantee ***,our analysis demonstrates that within the fidelity threshold,this algorithm can significantly reduce transmission burden while maintaining the same convergence rate order as its no-compression *** experiments further validate the theoretical findings by demonstrating that CHOCO-SGD improves communication efficiency and keeps the same convergence rate order *** experiments also show that the algorithm fails to converge with low compression fidelity and in time-varying ***,our study offers valuable insights into the potential applicability of CHOCO-SGD for non-strongly convex ***,we provide practical guidelines for researchers seeking to utilize this algorithm in real-world scenarios.

关键词： Distributed stochastic optimization arbitrary compression fidelity non-strongly convex objective function

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