Learning Convex Optimization Models

Akshay Agrawal

doi:10.1109/JAS.2021.1004075

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Learning Convex Optimization Models

2021-08-01

Akshay Agrawal

Shane Barratt *

Stephen Boyd

DOI：10.1109/JAS.2021.1004075

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Abstract

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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.

Keywords:

Predictive models

Convex functions

Numerical models

Logistics

Convex optimization

differentiable optimization

machine learning

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