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An efficient primal dual prox method for non-smooth optimization
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DOI：10.1007/s10994-014-5436-1.png)
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摘要
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We study 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 a simple yet efficient method for a family of non-smooth optimization problems 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 assuming that the proximal step can be efficiently solved, significantly faster than a standard subgradient descent method that has an convergence rate. Our empirical studies verify the efficiency of the proposed method for various non-smooth optimization problems that arise ubiquitously in machine learning by comparing it to the state-of-the-art first order methods.
Keyword:
Non-smooth optimization
Primal dual method
Convergence rate
Sparsity
Efficiency
期刊
IF:
2.9
论文数:
2.7K
被引数:
3.4W
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