Invited Talk: Understanding the Role of Optimism in Minimax Optimization: A Proximal Point Approach

by · Dec 14, 2019 · 148 views ·

In this talk, we consider solving saddle point problems, and, in particular, we discuss the concept of “optimism” or “negative momentum” - a technique which is observed to have superior empirical performance in training GANs. The goal of this talk is to provide a theoretical understanding on why optimism helps, in particular why the Optimistic Gradient Descent Ascent (OGDA) algorithm performs well in practice. To do so, we first consider the classical Proximal Point algorithm which is an implicit algorithm to solve this problem. We then show that OGDA inherently tries to approximate the proximal point method, and this is the rationale behind the ‘’negative momentum” term in the update of OGDA. This proximal point approximation viewpoint also enables us to provide a much simpler analysis of another well studied algorithm - the Extra-Gradient (EG) method.