We develop a principled approach to end-to-end learning in stochastic optimization. First, we show that the standard end-to-end learning algorithm admits a Bayesian interpretation and trains a posterior Bayes action map. Building on the insights of this analysis, we then propose new end-to-end learning algorithms for training decision maps that output solutions of empirical risk minimization and distributionally robust optimization problems, two dominant modeling paradigms in optimization under uncertainty. Numerical results for a synthetic newsvendor problem illustrate the key differences between alternative training schemes. We also investigate an economic dispatch problem based on real data to showcase the impact of the neural network architecture of the decision maps on their test performance.

翻译：我们提出了一种在随机优化中进行端到端学习的严谨方法。首先，我们证明标准端到端学习算法具有贝叶斯解释，并训练了一个后验贝叶斯行动映射。基于这一分析的见解，我们随后提出了新的端到端学习算法，用于训练输出经验风险最小化和分布鲁棒优化问题（不确定性优化中的两种主要建模范式）解的决策映射。针对一个合成报童问题的数值结果揭示了不同训练方案之间的关键差异。我们还基于真实数据研究了一个经济调度问题，以展示决策映射的神经网络架构对其测试性能的影响。