Learning to Stop: Deep Learning for Mean Field Optimal Stopping

Lorenzo Magnino, Yuchen Zhu, Mathieu Lauriere
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:42453-42486, 2025.

Abstract

Optimal stopping is a fundamental problem in optimization with applications in risk management, finance, robotics, and machine learning. We extend the standard framework to a multi-agent setting, named multi-agent optimal stopping (MAOS), where agents cooperate to make optimal stopping decisions in a finite-space, discrete-time environment. Since solving MAOS becomes computationally prohibitive as the number of agents is very large, we study the mean-field optimal stopping (MFOS) problem, obtained as the number of agents tends to infinity. We establish that MFOS provides a good approximation to MAOS and prove a dynamic programming principle (DPP) based on mean-field control theory. We then propose two deep learning approaches: one that learns optimal stopping decisions by simulating full trajectories and another that leverages the DPP to compute the value function and to learn the optimal stopping rule using backward induction. Both methods train neural networks to approximate optimal stopping policies. We demonstrate the effectiveness and the scalability of our work through numerical experiments on 6 different problems in spatial dimension up to 300. To the best of our knowledge, this is the first work to formalize and computationally solve MFOS in discrete time and finite space, opening new directions for scalable MAOS methods. Code is available at https://github.com/yuchen-zhu-zyc/Learning-to-Stop

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-magnino25a, title = {Learning to Stop: Deep Learning for Mean Field Optimal Stopping}, author = {Magnino, Lorenzo and Zhu, Yuchen and Lauriere, Mathieu}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {42453--42486}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/magnino25a/magnino25a.pdf}, url = {https://proceedings.mlr.press/v267/magnino25a.html}, abstract = {Optimal stopping is a fundamental problem in optimization with applications in risk management, finance, robotics, and machine learning. We extend the standard framework to a multi-agent setting, named multi-agent optimal stopping (MAOS), where agents cooperate to make optimal stopping decisions in a finite-space, discrete-time environment. Since solving MAOS becomes computationally prohibitive as the number of agents is very large, we study the mean-field optimal stopping (MFOS) problem, obtained as the number of agents tends to infinity. We establish that MFOS provides a good approximation to MAOS and prove a dynamic programming principle (DPP) based on mean-field control theory. We then propose two deep learning approaches: one that learns optimal stopping decisions by simulating full trajectories and another that leverages the DPP to compute the value function and to learn the optimal stopping rule using backward induction. Both methods train neural networks to approximate optimal stopping policies. We demonstrate the effectiveness and the scalability of our work through numerical experiments on 6 different problems in spatial dimension up to 300. To the best of our knowledge, this is the first work to formalize and computationally solve MFOS in discrete time and finite space, opening new directions for scalable MAOS methods. Code is available at https://github.com/yuchen-zhu-zyc/Learning-to-Stop} }
Endnote
%0 Conference Paper %T Learning to Stop: Deep Learning for Mean Field Optimal Stopping %A Lorenzo Magnino %A Yuchen Zhu %A Mathieu Lauriere %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-magnino25a %I PMLR %P 42453--42486 %U https://proceedings.mlr.press/v267/magnino25a.html %V 267 %X Optimal stopping is a fundamental problem in optimization with applications in risk management, finance, robotics, and machine learning. We extend the standard framework to a multi-agent setting, named multi-agent optimal stopping (MAOS), where agents cooperate to make optimal stopping decisions in a finite-space, discrete-time environment. Since solving MAOS becomes computationally prohibitive as the number of agents is very large, we study the mean-field optimal stopping (MFOS) problem, obtained as the number of agents tends to infinity. We establish that MFOS provides a good approximation to MAOS and prove a dynamic programming principle (DPP) based on mean-field control theory. We then propose two deep learning approaches: one that learns optimal stopping decisions by simulating full trajectories and another that leverages the DPP to compute the value function and to learn the optimal stopping rule using backward induction. Both methods train neural networks to approximate optimal stopping policies. We demonstrate the effectiveness and the scalability of our work through numerical experiments on 6 different problems in spatial dimension up to 300. To the best of our knowledge, this is the first work to formalize and computationally solve MFOS in discrete time and finite space, opening new directions for scalable MAOS methods. Code is available at https://github.com/yuchen-zhu-zyc/Learning-to-Stop
APA
Magnino, L., Zhu, Y. & Lauriere, M.. (2025). Learning to Stop: Deep Learning for Mean Field Optimal Stopping. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:42453-42486 Available from https://proceedings.mlr.press/v267/magnino25a.html.

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