Revisiting frank-wolfe for polytopes: Strict complementarity and sparsity

نتاج البحث: نشر في مجلةمقالة من مؤنمرمراجعة النظراء

ملخص

In recent years it was proved that simple modifications of the classical Frank-Wolfe algorithm (aka conditional gradient algorithm) for smooth convex minimization over convex and compact polytopes, converge with linear rate, assuming the objective function has the quadratic growth property. However, the rate of these methods depends explicitly on the dimension of the problem which cannot explain their empirical success for large scale problems. In this paper we first demonstrate that already for very simple problems and even when the optimal solution lies on a low-dimensional face of the polytope, such dependence on the dimension cannot be avoided in worst case. We then revisit the addition of a strict complementarity assumption already considered in Wolfe’s classical book [29], and prove that under this condition, the Frank-Wolfe method with away-steps and line-search converges linearly with rate that depends explicitly only on the dimension of the optimal face. We motivate strict complementarity by proving that it implies sparsity-robustness of optimal solutions to noise.

اللغة الأصليةالإنجليزيّة
دوريةAdvances in Neural Information Processing Systems
مستوى الصوت2020-December
حالة النشرنُشِر - 2020
الحدث34th Conference on Neural Information Processing Systems, NeurIPS 2020 - Virtual, Online
المدة: ٦ ديسمبر ٢٠٢٠١٢ ديسمبر ٢٠٢٠

All Science Journal Classification (ASJC) codes

  • !!Computer Networks and Communications
  • !!Information Systems
  • !!Signal Processing

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