Learning Convex Optimization Models Article Swipe

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Convex optimization Mathematical optimization Conic optimization Proper convex function Optimization problem Regular polygon Heuristic Maximization Convex analysis Convex combination A priori and a posteriori Mathematics Computer science Epistemology Philosophy Geometry

Akshay Agrawal , Shane Barratt , Stephen Boyd ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.1109/jas.2021.1004075 · OA: W3033534062

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: Convex optimization · Mathematical optimization · Conic optimization · Proper convex function · Optimization problem · Regular polygon · Heuristic · Maximization · Convex analysis · Convex combination · A priori and a posteriori · Mathematics · Computer science