ResearchTrend.AI
  • Papers
  • Communities
  • Events
  • Blog
  • Pricing
Papers
Communities
Social Events
Terms and Conditions
Pricing
Parameter LabParameter LabTwitterGitHubLinkedInBlueskyYoutube

© 2025 ResearchTrend.AI, All rights reserved.

  1. Home
  2. Papers
  3. 1201.5283
133
36
v1v2v3v4v5 (latest)

An Efficient Primal-Dual Prox Method for Non-Smooth Optimization

24 January 2012
Tianbao Yang
M. Mahdavi
Rong Jin
Shenghuo Zhu
ArXiv (abs)PDFHTML
Abstract

We consider the non-smooth optimization problems in machine learning, where both the loss function and the regularizer are non-smooth functions. Previous studies on efficient empirical loss minimization assume either a smooth loss function or a strongly convex regularizer, making them unsuitable for non-smooth optimization. We develop an efficient method for a family of non-smooth optimization where the dual form of the loss function is bilinear in primal and dual variables. We cast a non-smooth optimization problem into a minimax optimization problem, and develop a primal dual prox method that solves the minimax optimization problem at a rate of O(1/T)O(1/T)O(1/T), significantly faster than a standard gradient descent method (O(1/T)O(1/\sqrt{T})O(1/T​)). Our empirical study verifies the efficiency of the proposed method for non-smooth optimization by comparing it to the state-of-the-art first order methods.

View on arXiv
Comments on this paper