Stochastic Frank-Wolfe Methods for Nonconvex Optimization
This work addresses optimization challenges in machine learning for scenarios with structured constraints, offering incremental improvements in convergence efficiency.
The paper tackles the problem of applying Frank-Wolfe methods to nonconvex stochastic and finite-sum optimization, proposing new variance-reduced algorithms that achieve provably faster convergence rates than classical methods.
We study Frank-Wolfe methods for nonconvex stochastic and finite-sum optimization problems. Frank-Wolfe methods (in the convex case) have gained tremendous recent interest in machine learning and optimization communities due to their projection-free property and their ability to exploit structured constraints. However, our understanding of these algorithms in the nonconvex setting is fairly limited. In this paper, we propose nonconvex stochastic Frank-Wolfe methods and analyze their convergence properties. For objective functions that decompose into a finite-sum, we leverage ideas from variance reduction techniques for convex optimization to obtain new variance reduced nonconvex Frank-Wolfe methods that have provably faster convergence than the classical Frank-Wolfe method. Finally, we show that the faster convergence rates of our variance reduced methods also translate into improved convergence rates for the stochastic setting.