Abstracts

Tobias Sutter:
Recursive Frank-Wolfe Optimization with Learned Domains and Objectives

We study a data-driven variant of the classical Frank-Wolfe algorithm for convex optimization over compact convex domains. In contrast to the standard setting, both the feasible domain and the objective function are initially unknown and must be learned from data during the optimization process. Our method incorporates statistical estimators directly into the Frank-Wolfe iterations, thereby preserving the projection-free nature of the classical algorithm while adapting to uncertainty in the problem formulation. We prove convergence guarantees showing that the optimization error is controlled by the accuracy of the learned domain and objective estimators. Numerical experiments illustrate that the proposed recursive Frank-Wolfe method can achieve convergence behavior comparable to the classical algorithm with exact problem knowledge, while offering significant computational savings in data-driven settings.

This is joint work with Marcel Kaiser, University of Konstanz.