Topology-aware Generalization of Decentralized SGD

@article{Zhu2022TopologyawareGO,
  title={Topology-aware Generalization of Decentralized SGD},
  author={Tongtian Zhu and Fengxiang He and Lance Zhang and Zhengyang Niu and Mingli Song and Dacheng Tao},
  journal={ArXiv},
  year={2022},
  volume={abs/2206.12680}
}
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 ( m/N +1 /m + λ 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 − λ is the spectral gap that measures the connectivity of the communication topology. These results then deliver an O (1 /N +(( m − 1 λ 2 ) α 2 + m − α ) /N 1… 

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