Global Convergence of Frank Wolfe on One Hidden Layer Networks

Alexandre d'Aspremont (1, 2, 3, 4) , Mert Pilanci (5)

1 SIERRA - Statistical Machine Learning and Parsimony
2 CNRS - Centre National de la Recherche Scientifique
3 LIENS - Laboratoire d'informatique de l'école normale supérieure
4 PSL - Université Paris Sciences et Lettres
5 Stanford University

We derive global convergence bounds for the Frank Wolfe algorithm when training one hidden layer neural networks. When using the ReLU activation function, and under tractable preconditioning assumptions on the sample data set, the linear minimization oracle used to incrementally form the solution can be solved explicitly as a second order cone program. The classical Frank Wolfe algorithm then converges with rate $O(1/T)$ where $T$ is both the number of neurons and the number of calls to the oracle.

Domaines: Machine Learning [stat.ML]; Recherche opérationnelle [math.OC]

Alexandre d'Aspremont, Mert Pilanci. Global Convergence of Frank Wolfe on One Hidden Layer Networks. 2020. ⟨hal-02983259⟩