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Geometric Descent Method for Convex Composite Minimization
Shixiang Chen · Shiqian Ma · Wei Liu

Tue Dec 05 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #170
In this paper, we extend the geometric descent method recently proposed by Bubeck, Lee and Singh to tackle nonsmooth and strongly convex composite problems. We prove that our proposed algorithm, dubbed geometric proximal gradient method (GeoPG), converges with a linear rate $(1-1/\sqrt{\kappa})$ and thus achieves the optimal rate among first-order methods, where $\kappa$ is the condition number of the problem. Numerical results on linear regression and logistic regression with elastic net regularization show that GeoPG compares favorably with Nesterov's accelerated proximal gradient method, especially when the problem is ill-conditioned.

Author Information

Shixiang Chen (The Chinese University of HongKong)
Shiqian Ma (UC Davis)
Wei Liu (Tencent AI Lab)

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