Papers › Topology-aware Generalization of Decentralized SGD

Topology-aware Generalization of Decentralized SGD

25 Jun 2022arXiv:2206.12680archive 2025-07-28

Tongtian Zhu, Fengxiang He, Lan Zhang, Zhengyang Niu, Mingli Song, DaCheng Tao

This paper studies the algorithmic stability and generalizability of decentralized stochastic gradient descent (D-SGD). We prove that the consensus model learned by D-SGD is 𝒪(N⁻¹+m⁻¹ +λ²)-stable in expectation in the non-convex non-smooth setting, where N is the total sample size, m is the worker number, and 1+λ is the spectral gap that measures the connectivity of the communication topology. These results then deliver an 𝒪(N^(-(1+α)/2)+ m^(-(1+α)/2)+λ^(1+α) + ϕ_𝒮) in-average generalization bound, which is non-vacuous even when λ is closed to $1$, in contrast to vacuous as suggested by existing literature on the projected version of D-SGD. Our theory indicates that the generalizability of D-SGD is positively correlated with the spectral gap, and can explain why consensus control in initial training phase can ensure better generalization. Experiments of VGG-11 and ResNet-18 on CIFAR-10, CIFAR-100 and Tiny-ImageNet justify our theory. To our best knowledge, this is the first work on the topology-aware generalization of vanilla D-SGD. Code is available at https://github.com/Raiden-Zhu/Generalization-of-DSGD.

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