Generalization of Decentralized Gradient Descent with Separable Data

Decentralized learning offers privacy and communication efficiency when data are naturally distributed among agents communicating over an underlying graph. Motivated by overparameterized learning settings, in which models are trained to zero training loss, we study algorithmic and generalization properties of decentralized learning with gradient descent on separable data. Specifically, for decentralized gradient descent (DGD) and a variety of loss functions that asymptote to zero at infinity (including exponential and logistic losses), we derive novel finite-time generalization bounds. This complements a long line of recent work that studies the generalization performance and the implicit bias of gradient descent over separable data, but has thus far been limited to centralized learning scenarios. Notably, our generalization bounds match in order their centralized counterparts. Critical behind this, and of independent interest, is establishing novel bounds on the training loss and the rate-of-consensus of DGD for a class of self-bounded losses. Finally, we conduct numerical experiments which corroborate our theoretical results.