End-to-End Learning for Stochastic Optimization: A Bayesian Perspective

Yves Rychener, Daniel Kuhn, Tobias Sutter
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:29455-29472, 2023.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-rychener23a, title = {End-to-End Learning for Stochastic Optimization: A {B}ayesian Perspective}, author = {Rychener, Yves and Kuhn, Daniel and Sutter, Tobias}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {29455--29472}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/rychener23a/rychener23a.pdf}, url = {https://proceedings.mlr.press/v202/rychener23a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T End-to-End Learning for Stochastic Optimization: A Bayesian Perspective %A Yves Rychener %A Daniel Kuhn %A Tobias Sutter %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-rychener23a %I PMLR %P 29455--29472 %U https://proceedings.mlr.press/v202/rychener23a.html %V 202 %X 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.
APA
Rychener, Y., Kuhn, D. & Sutter, T.. (2023). End-to-End Learning for Stochastic Optimization: A Bayesian Perspective. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:29455-29472 Available from https://proceedings.mlr.press/v202/rychener23a.html.

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