Shifted divergences for sampling, privacy, and beyond

Abstract

Shifted divergences provide a principled way of making information theoretic divergences (e.g. KL) geometrically aware via optimal transport smoothing. In this talk, I will argue that shifted divergences provide a powerful approach towards unifying optimization, sampling, privacy, and beyond. For concreteness, I will demonstrate these connections via three recent highlights. (1) Characterizing the differential privacy of Noisy-SGD, the standard algorithm for private convex optimization. (2) Characterizing the mixing time of the Langevin Algorithm to its stationary distribution for log-concave sampling. (3) The fastest high-accuracy algorithm for sampling from log-concave distributions. A recurring theme is a certain notion of algorithmic stability, and the central technique for establishing this is shifted divergences. Based on joint work with Kunal Talwar, and with Sinho Chewi.

Date
2023, Oct 12 10:00 AM PDT
Event
KI Seminar
Location
Online (zoom)
Registration
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