Fast Saddle-Point Algorithm for Generalized Dantzig Selector and FDR Control with the Ordered l1-Norm

Abstract

In this paper we propose a primal-dual proximal extragradient algorithm to solve the generalized Dantzig selector (GDS) estimation problem, based on a new convex-concave saddle-point (SP) reformulation. Our new formulation makes it possible to adopt recent developments in saddle-point optimization, to achieve the optimal $O(1/k)$ rate of convergence. Compared to the optimal non-SP algorithms, ours do not require specification of sensitive parameters that affect algorithm performance or solution quality. We also provide a new analysis showing a possibility of local acceleration to achieve the rate of $O(1/k^2)$ in special cases even without strong convexity or strong smoothness. As an application, we propose a GDS equipped with the ordered ${\ell }_1$-norm, showing its false discovery rate control properties in variable selection. Algorithm performance is compared between ours and other alternatives, including the linearized ADMM, Nesterov's smoothing, Nemirovski's mirror-prox, and the accelerated hybrid proximal extragradient techniques.

arXiv commentIn AISTATS 2016

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• SLOPE - Adaptive variable selection via convex optimization
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Cited by in corpus (1)

• Structure Learning of Gaussian Markov Random Fields with False Discovery Rate Control