Learning Convex Optimization Models

2020/06/07 by Akshay Agrawal, Agrawal, Akshay, Shane Barratt +3 · 5 citations
Computer Science · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #cs.LG #stat.ML

paper · pdf · doi:10.48550/arxiv.2006.04248

Authors listed in alphabetical order

arxiv created 2020/06/18 · arxiv updated 2020/06/19

Abstract

A convex optimization model predicts an output from an input by solving a convex optimization problem. The class of convex optimization models is large, and includes as special cases many well-known models like linear and logistic regression. We propose a heuristic for learning the parameters in a convex optimization model given a dataset of input-output pairs, using recently developed methods for differentiating the solution of a convex optimization problem with respect to its parameters. We describe three general classes of convex optimization models, maximum a posteriori (MAP) models, utility maximization models, and agent models, and present a numerical experiment for each.

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