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.

为了在随机优化中实现端对端学习，我们发展了一种基于贝叶斯解释的算法，并提出了一种训练决策映射的全新算法，用于输出经验风险最小化和分布式鲁棒优化问题的解决方案。通过对合成售货员问题和基于真实数据的经济调度问题进行数值实验，阐明了替代培训方案之间的关键差异以及决策映射的神经网络架构对测试性能的影响。

基于贝叶斯视角的随机优化端到端学习