Topology-aware Generalization of Decentralized SGD

• URL: http://arxiv.org/abs/2206.12680v2
• Date: Tue, 28 Jun 2022 12:40:49 GMT
• Title: Topology-aware Generalization of Decentralized SGD
• Authors: Tongtian Zhu, Fengxiang He, Lan Zhang, Zhengyang Niu, Mingli Song, Dacheng Tao
• Abstract summary: This paper studies the generalizability of decentralized Valpha-10 stability descent (D-SGD) We prove that the generalizability of D-SGD has a positive correlation with connectivity in initial training phase.
• Score: 89.25765221779288
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\mathcal{O}{(m/N+1/m+\lambda^2)}$-stable in expectation in the non-convex non-smooth setting, where $N$ is the total sample size of the whole system, $m$ is the worker number, and $1-\lambda$ is the spectral gap that measures the connectivity of the communication topology. These results then deliver an $\mathcal{O}{(1/N+{({(m^{-1}\lambda^2)}^{\frac{\alpha}{2}}+ m^{-\alpha})}/{N^{1-\frac{\alpha}{2}}})}$ in-average generalization bound, which is non-vacuous even when $\lambda$ 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 has a positive correlation 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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