End-to-End Learning for Stochastic Optimization: A Bayesian Perspective
- URL: http://arxiv.org/abs/2306.04174v2
- Date: Sun, 11 Jun 2023 10:29:32 GMT
- Title: End-to-End Learning for Stochastic Optimization: A Bayesian Perspective
- Authors: Yves Rychener, Daniel Kuhn, Tobias Sutter
- Abstract summary: We develop a principled approach to end-to-end learning in optimization.
We show that the standard end-to-end learning algorithm admits a Bayesian interpretation and trains a posterior Bayes action map.
We then propose new end-to-end learning algorithms for training decision maps.
- Score: 9.356870107137093
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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