Stability and Generalization of the Decentralized Stochastic Gradient Descent
This work provides foundational theoretical understanding of decentralized SGD, which is important for researchers and practitioners working with distributed machine learning systems.
This paper provides a novel formulation of decentralized stochastic gradient descent and, using (non)convex optimization theory, establishes the first stability and generalization guarantees for this method. The theoretical results indicate that decentralization deteriorates the stability of SGD.
The stability and generalization of stochastic gradient-based methods provide valuable insights into understanding the algorithmic performance of machine learning models. As the main workhorse for deep learning, stochastic gradient descent has received a considerable amount of studies. Nevertheless, the community paid little attention to its decentralized variants. In this paper, we provide a novel formulation of the decentralized stochastic gradient descent. Leveraging this formulation together with (non)convex optimization theory, we establish the first stability and generalization guarantees for the decentralized stochastic gradient descent. Our theoretical results are built on top of a few common and mild assumptions and reveal that the decentralization deteriorates the stability of SGD for the first time. We verify our theoretical findings by using a variety of decentralized settings and benchmark machine learning models.