Events

Math and Data Seminar: Privacy of Noisy SGD

Speaker: Jason Altschuler

Location: 60 Fifth Avenue, Room 150

Date: Thursday, September 15, 2022

A central issue in machine learning is how to train models on sensitive user data. Industry has widely adopted a simple algorithm: Stochastic Gradient Descent with noise (aka Stochastic Gradient Langevin Dynamics). However, foundational theoretical questions about this algorithm’s privacy loss remain open—even in the seemingly simple setting of smooth convex losses over a bounded domain. Our main result resolves these questions: for a large range of parameters, we characterize the differential privacy up to a constant factor. This result reveals that all previous analyses for this setting have the wrong qualitative behavior. Specifically, while previous privacy analyses increase ad infinitum in the number of iterations, we show that after a small burn-in period, running SGD longer leaks no further privacy.