Accelerating Nonconvex Optimization via Online Learning

Aryan Mokhtari, UT Austin

A fundamental problem in optimization is finding an ε-first-order stationary point of a smooth function using only gradient information. The best-known gradient query complexity for this task, assuming both the gradient and Hessian of the objective function are Lipschitz continuous, is O( ε^(−7/4) ). In this talk, I present a method with a gradient complexity of O( d^(1/4) ε^(−13/8) ), where d is the problem dimension—yielding improved complexity when d = O( ε^(−1/2) ). The proposed method builds on quasi-Newton ideas and operates by solving two online learning problems under the hood.