A Recursive Domain- and Objective-Adaptive Frank-Wolfe Algorithm

Abstract

We investigate a recursive variant of the classical Frank-Wolfe algorithm for minimizing a convex differentiable function over a convex compact domain. Unlike the traditional setting, we assume that both the problem domain and the objective function are initially unknown and must be learned from data. To address this, we integrate estimators into the optimization process, allowing the algorithm to iteratively refine approximations of the problem domain and the objective function. Our approach maintains the projection-free nature of the classical Frank-Wolfe algorithm while adapting to the uncertainty inherent in data-driven settings. We establish convergence guarantees for the recursive method, showing that the optimization error scales with the accuracy of the learned estimators. Two experiments support our theoretical findings, demonstrating that the proposed method achieves convergence behavior comparable to that of the classical Frank-Wolfe algorithm under exact knowledge of the problem domain and objective function, while offering significant computational savings.