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Learning Convex Optimization Models
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DOI：10.1109/JAS.2021.1004075.png)
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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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