Fast Optimization Methods for L1-Regularization: A Comparative Study and 2 New Approaches

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Authors Mark W. Schmidt1, Glenn Fung2, RĂ³mer Rosales2 1University of British Columbia, 2Siemens
Journal/Conference Name EUROPEAN CONFERENCE ON MACHINE LEARNING
Paper Category
Paper Abstract L1 regularization is effective for feature selection, but the resulting optimization is challenging due to the non-differentiability of the 1-norm. In this paper we compare state-of-the-art optimization techniques to solve this problem across several loss functions. Furthermore, we propose two new techniques. The first is based on a smooth (differentiable) convex approximation for the L1 regularizer that does not depend on any assumptions about the loss function used. The other technique is a new strategy that addresses the non-differentiability of the L1-regularizer by casting the problem as a constrained optimization problem that is then solved using a specialized gradient projection method. Extensive comparisons show that our newly proposed approaches consistently rank among the best in terms of convergence speed and efficiency by measuring the number of function evaluations required.
Date of publication 2007
Code Programming Language MATLAB
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