Information-Theoretic Generalization Bounds for Stochastic Gradient Descent

February 18, 2022

Gergely Neu


Information-Theoretic Generalization Bounds for Stochastic Gradient Descent

Time:   11:00am
Location:   Meeting room 302
Virtual transmission:   Zoom3 https://zoom.us/j/3911012202
Pass:   5551337

We study the generalization properties of the popular stochastic optimization method known as stochastic gradient descent (SGD) for optimizing general non-convex loss functions. Our main contribution is providing upper bounds on the generalization error that depend on local statistics of the stochastic gradients evaluated along the path of iterates calculated by SGD. The key factors our bounds depend on are the variance of the gradients (with respect to the data distribution) and the local smoothness of the objective function along the SGD path, and the sensitivity of the loss function to perturbations to the final output. Our key technical tool is combining the information-theoretic generalization bounds previously used for analyzing randomized variants of SGD with a perturbation analysis of the iterates.