A Frank-Wolfe Algorithm for Oracle-based Robust Optimization

TL;DR

This paper introduces a Frank-Wolfe algorithm tailored for oracle-based robust optimization, effectively handling objective uncertainty and outperforming existing methods in high-dimensional scenarios.

Contribution

It presents a novel iterative Frank-Wolfe algorithm for oracle-based robust optimization, achieving optimal oracle complexity and improved performance on large-scale problems.

Findings

Attains the best known oracle complexity for the problem.

Performs better than state-of-the-art methods on high-dimensional instances.

Effective for larger uncertainty sets.

Abstract

We tackle robust optimization problems under objective uncertainty in the oracle model, i.e., when the deterministic problem is solved by an oracle. The oracle-based setup is favorable in many situations, e.g., when a compact formulation of the feasible region is unknown or does not exist. We propose an iterative method based on a Frank-Wolfe type algorithm applied to a smoothed version of the piecewise linear objective function. Our approach bridges several previous efforts from the literature, attains the best known oracle complexity for the problem and performs better than state-of-the-art on high-dimensional problem instances, in particular for larger uncertainty sets.