ISyE Statistics Seminar: Stochastic convex optimization using mirror averaging algorithms

GUEST LECTURER
Dr. Philippe Rigollet

AFFILIATION
School of Mathematics, Georgia Tech

ABSTRACT
Several statistical problems where the goal is to minimize an unknown convex risk function, can be formulated in the general framework of stochastic convex optimization. For example, density estimation, regression and convex classification can be treated using the machinery of stochastic optimization. We describe a family of general algorithms called "mirror averaging algorithms" that yields and estimator (or a classifier) which attains optimal rates of convergence in several interesting cases. These optimal rates are illustrated on several examples and compared to standard estimators or classifiers.