Topology-aware Generalization of Decentralized SGD

Code

• github.com/raiden-zhu/generalization-of-dsgd
  OfficialIn paperpytorch★ 36

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 O(N^-1+m^-1 +^2)-stable in expectation in the non-convex non-smooth setting, where N is the total sample size, m is the worker number, and 1+ is the spectral gap that measures the connectivity of the communication topology. These results then deliver an O(N^-(1+)/2+ m^-(1+)/2+^1+ + _S) in-average generalization bound, which is non-vacuous even when 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.

Reproductions