Learning Convex Optimization Models
This work addresses the challenge of parameter estimation in convex optimization models for researchers and practitioners in machine learning and optimization, but it appears incremental as it builds on existing differentiation techniques.
The authors tackled the problem of learning parameters for convex optimization models from input-output data, achieving this by using methods to differentiate convex optimization solutions with respect to parameters, as demonstrated through numerical experiments on three model classes.
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.