Nonsmoothness in Machine Learning: specific structure, proximal identification, and applications

Abstract

Nonsmoothness is often a curse for optimization; but it is sometimes a blessing, in particular for applications in machine learning. In this paper, we present the specific structure of nonsmooth optimization problems appearing in machine learning and illustrate how to leverage this structure in practice, for compression, acceleration, or dimension reduction. We pay a special attention to the presentation to make it concise and easily accessible, with both simple examples and general results.

References in corpus (5)

• SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives
• Consistency of trace norm minimization
• Safe Feature Elimination for the LASSO and Sparse Supervised Learning Problems
• Local Convergence Properties of SAGA/Prox-SVRG and Acceleration
• Model Consistency for Learning with Mirror-Stratifiable Regularizers