End-to-End Learning for Stochastic Optimization: A Bayesian Perspective
This work addresses stochastic optimization challenges for researchers and practitioners, offering incremental improvements through new algorithms and insights.
The paper tackles the problem of end-to-end learning in stochastic optimization by providing a Bayesian interpretation of standard algorithms and proposing new ones for empirical risk minimization and distributionally robust optimization. Results include numerical illustrations on a synthetic newsvendor problem and real-data tests on an economic dispatch problem, showing the impact of neural network architectures on performance.
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.