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.

中文翻译：

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学习凸优化模型

凸优化模型通过求解凸优化问题来预测输入的输出。凸优化模型的类别很大，并且包括许多著名的模型，例如线性和逻辑回归作为特殊情况。我们提出了一种启发式方法，用于在给定输入-输出对数据集的情况下学习凸优化模型中的参数，使用最近开发的方法来区分凸优化问题的参数解。我们描述了三类通用的凸优化模型、最大后验 (MAP) 模型、效用最大化模型和代理模型，并为每个模型提供了数值实验。