Learning Convex Optimization Models

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.

Automated summary

Convex optimization models predict outputs by solving convex optimization problems, including well-known models like linear and logistic regression. The paper proposes a heuristic for learning parameters in convex optimization models and describes three general classes of such models, presenting numerical experiments for each.