Projection-Free Adaptive Gradients for Large-Scale Optimization

• URL: http://arxiv.org/abs/2009.14114v3
• Date: Mon, 15 Feb 2021 14:38:10 GMT
• Title: Projection-Free Adaptive Gradients for Large-Scale Optimization
• Authors: Cyrille W. Combettes and Christoph Spiegel and Sebastian Pokutta
• Abstract summary: Frank-Wolfe algorithms occupy a unique position as they alleviate both computational burdens by querying only approximate first-order information from the objective. We show that our method can improve the performance of adaptive algorithms for constrained optimization.
• Score: 22.0439695290991
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The complexity in large-scale optimization can lie in both handling the objective function and handling the constraint set. In this respect, stochastic Frank-Wolfe algorithms occupy a unique position as they alleviate both computational burdens, by querying only approximate first-order information from the objective and by maintaining feasibility of the iterates without using projections. In this paper, we improve the quality of their first-order information by blending in adaptive gradients. We derive convergence rates and demonstrate the computational advantage of our method over the state-of-the-art stochastic Frank-Wolfe algorithms on both convex and nonconvex objectives. The experiments further show that our method can improve the performance of adaptive gradient algorithms for constrained optimization.

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