Nov 21 (Mon) @ 1:00pm: "Minmax Optimization: New Applications and Algorithms," Raphael Chinchilla, ECE PhD Defense

Abstract

Minmax optimization is widely used in robust model predictive control, computer security problems, robust training of neural networks, generative adversarial networks, reformulating stochastic programming as min-max optimization, and robust stochastic programs. In the first part of this talk, we recapitulate some of the results presented in the qualification examination, where we show a relation between stochastic and minmax optimization. In the second part, we address the design of algorithms to solve nonconvex-nonconcave minmax optimizations using second order methods. These algorithms modify the Hessian matrix to obtain a search direction that can be seen as the solution to a quadratic program that locally approximates the minmax problem. We show that by selecting this type of modification appropriately, the only stable points of the resulting iterations are local minmax points. For minmax model predictive control problems, these algorithms leads to computation times that scale linearly with the horizon length.

Bio

Raphael Chinchilla received a B.Eng. from Escola Politécnica da Universidade de São Paulo, Brazil, in 2016; a M.Sc. from University Paris-Saclay, France, in 2016; a Diplôme d’Ingénieur (M.Sc.) from Télécom Paris, France, in 2016; and a M.Sc. from the University of California, Santa Barbara, in 2021; all in electrical engineering.

He currently is a Ph.D candidate at the Center for Control, Dynamical Systems and Computation at the University of California, Santa Barbara, where he researches algorithms and application for nonconvex-nonconcave minmax optimization with application in machine learning, control and estimation. Chinchilla has been an active member in his academic communities, having served as a student representative in multiple committees in all universities he attended. He was the first international student elected to the Graduate Student Association at UCSB, as Vice President of Academic Affairs, co-founder of the Electrical and Computer Engineering Graduate Student Association at UCSB, and was a Director of Academic Affairs at the Electrical Engineering Students Association (CEE Poli) at USP. Beyond academic communities, Chinchilla is also an active member of the Isla Vista Food Co-op, where he is a board member and the Chief Financial Officer.

Hosted by: Professor João Hespanha

Submitted by: Raphael Chinchilla <raphaelchinchilla@ucsb.edu>