Departamento de Matemáticas UAM

Lunes, 25 de abril de 2022, 13:00-14:00  (horario diferente al habitual!!!!)

Enlace:  https://us06web.zoom.us/j/85740874805?pwd=dGFSQi8xREFMcHVTQjRBSlVmRSsxdz09

Ponente:   Nicolas Garcia Trillos (University of Wisconsin-Madison)

Título: The multimarginal optimal transport formulation of adversarial multiclass classification

Abstract: Adversarial training is a framework widely used by machine learning practitioners to enforce robustness of learning models. Despite the development of several computational strategies for adversarial training and some theoretical development in the broader distributionally robust optimization literature, there are still several theoretical questions about adversarial training that remain relatively unexplored. In this talk, I will discuss an equivalence between adversarial training in the context of non-parametric multiclass classification problems and multimarginal optimal transport problems. This is another analytical interpretation of adversarial training that expands recently studied connections to perimeter minimization problems. One of the implications of the connection discussed during the talk is computational: to solve a certain adversarial problem, we may as well solve a multimarginal optimal transport problem. We will discuss many of the nuances of this interpretation and of its computational consequences. This is joint work with my student Jakwang Kim (UW) and my colleague Matt Jacobs (Purdue).