What's in a Smoothness Constant? Tighter Rates for Local SGD with Bounded Second-order Heterogeneity
Local SGD, also known as Federated Averaging, is a widely used distributed optimization algorithm. Although Local SGD often outperforms alternatives such as Mini-batch SGD in practice, theory still only partially explains when and why local updates help under realistic data heterogeneity. Recent work by [Patel et al., 2025] shows that a bounded second-order heterogeneity assumption captures the efficiency of Local SGD for strongly convex objectives, and conjectures that the same principle extends to the general convex setting. In this paper, we prove this conjecture by establishing an improved convergence guarantee for Local SGD on general convex objectives under bounded second-order hete...
| Authors | Kumar Kshitij Patel, Rustem Islamov, Sebastian U Stich et al. |
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| Primary category | cs.LG |
| Published | 16 July 2026 |
| Last updated at source | 16 July 2026 |
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