Learning to Optimize with Stochastic Dominance Constraints

Hanjun Dai, Yuan Xue, Niao He, Yixin Wang, Na Li, Dale Schuurmans, Bo Dai
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:8991-9009, 2023.

Abstract

In real-world decision-making, uncertainty is important yet difficult to handle. Stochastic dominance provides a theoretically sound approach to comparing uncertain quantities, but optimization with stochastic dominance constraints is often computationally expensive, which limits practical applicability. In this paper, we develop a simple yet efficient approach for the problem, Light Stochastic Dominance Solver (light-SD), by leveraging properties of the Lagrangian. We recast the inner optimization in the Lagrangian as a learning problem for surrogate approximation, which bypasses the intractability and leads to tractable updates or even closed-form solutions for gradient calculations. We prove convergence of the algorithm and test it empirically. The proposed light-SD demonstrates superior performance on several representative problems ranging from finance to supply chain management.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-dai23b, title = {Learning to Optimize with Stochastic Dominance Constraints}, author = {Dai, Hanjun and Xue, Yuan and He, Niao and Wang, Yixin and Li, Na and Schuurmans, Dale and Dai, Bo}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {8991--9009}, year = {2023}, editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}, volume = {206}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v206/dai23b/dai23b.pdf}, url = {https://proceedings.mlr.press/v206/dai23b.html}, abstract = {In real-world decision-making, uncertainty is important yet difficult to handle. Stochastic dominance provides a theoretically sound approach to comparing uncertain quantities, but optimization with stochastic dominance constraints is often computationally expensive, which limits practical applicability. In this paper, we develop a simple yet efficient approach for the problem, Light Stochastic Dominance Solver (light-SD), by leveraging properties of the Lagrangian. We recast the inner optimization in the Lagrangian as a learning problem for surrogate approximation, which bypasses the intractability and leads to tractable updates or even closed-form solutions for gradient calculations. We prove convergence of the algorithm and test it empirically. The proposed light-SD demonstrates superior performance on several representative problems ranging from finance to supply chain management.} }
Endnote
%0 Conference Paper %T Learning to Optimize with Stochastic Dominance Constraints %A Hanjun Dai %A Yuan Xue %A Niao He %A Yixin Wang %A Na Li %A Dale Schuurmans %A Bo Dai %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-dai23b %I PMLR %P 8991--9009 %U https://proceedings.mlr.press/v206/dai23b.html %V 206 %X In real-world decision-making, uncertainty is important yet difficult to handle. Stochastic dominance provides a theoretically sound approach to comparing uncertain quantities, but optimization with stochastic dominance constraints is often computationally expensive, which limits practical applicability. In this paper, we develop a simple yet efficient approach for the problem, Light Stochastic Dominance Solver (light-SD), by leveraging properties of the Lagrangian. We recast the inner optimization in the Lagrangian as a learning problem for surrogate approximation, which bypasses the intractability and leads to tractable updates or even closed-form solutions for gradient calculations. We prove convergence of the algorithm and test it empirically. The proposed light-SD demonstrates superior performance on several representative problems ranging from finance to supply chain management.
APA
Dai, H., Xue, Y., He, N., Wang, Y., Li, N., Schuurmans, D. & Dai, B.. (2023). Learning to Optimize with Stochastic Dominance Constraints. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:8991-9009 Available from https://proceedings.mlr.press/v206/dai23b.html.

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