# Learning to Stop: Deep Learning for Mean Field Optimal Stopping

arXiv: https://arxiv.org/abs/2410.08850 · HTML: https://mlsanity.com/paper/2410.08850/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 54 references that are in the map.
- First posted on arXiv 11 Oct 2024.

## Builds on (most cited first, 28 of 28)

- [A Unified Algebraic Perspective on Lipschitz Neural Networks](https://mlsanity.com/paper/2303.03169/) (2023)
- [Model-Free Mean-Field Reinforcement Learning: Mean-Field MDP and Mean-Field Q-Learning](https://mlsanity.com/paper/1910.12802/) (2019)
- [Mean-Field Controls with Q-learning for Cooperative MARL: Convergence and Complexity Analysis](https://mlsanity.com/paper/2002.04131/) (2020)
- [Efficient Model-Based Multi-Agent Mean-Field Reinforcement Learning](https://mlsanity.com/paper/2107.04050/) (2021)
- [Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games: II -- The Finite Horizon Case](https://mlsanity.com/paper/1908.01613/) (2019)
- [On the Approximation of Cooperative Heterogeneous Multi-Agent Reinforcement Learning (MARL) using Mean Field Control (MFC)](https://mlsanity.com/paper/2109.04024/) (2021)
- [Linear-Quadratic Mean-Field Reinforcement Learning: Convergence of Policy Gradient Methods](https://mlsanity.com/paper/1910.04295/) (2019)
- [Optimal Stopping via Randomized Neural Networks](https://mlsanity.com/paper/2104.13669/) (2021)
- [Deep Learning Methods for Mean Field Control Problems with Delay](https://mlsanity.com/paper/1905.00358/) (2019)
- [Mean-field Markov decision processes with common noise and open-loop controls](https://mlsanity.com/paper/1912.07883/) (2019)
- [Dynamic Programming Principles for Mean-Field Controls with Learning](https://mlsanity.com/paper/1911.07314/) (2019)
- [Deep Learning for Mean Field Games and Mean Field Control with Applications to Finance](https://mlsanity.com/paper/2107.04568/) (2021)
- [Numerical resolution of McKean-Vlasov FBSDEs using neural networks](https://mlsanity.com/paper/1909.12678/) (2019)
- [Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics](https://mlsanity.com/paper/1604.04057/) (2016)
- [Proximal methods for stationary Mean Field Games with local couplings](https://mlsanity.com/paper/1608.07701/) (2016)
- [DeepSets and their derivative networks for solving symmetric PDEs](https://mlsanity.com/paper/2103.00838/) (2021)
- [Mean Field Markov Decision Processes](https://mlsanity.com/paper/2106.08755/) (2021)
- [A fast iterative PDE-based algorithm for feedback controls of nonsmooth mean-field control problems](https://mlsanity.com/paper/2108.06740/) (2021)
- [Mean-Field Optimal Control](https://mlsanity.com/paper/1306.5913/) (2013)
- [Learning Decentralized Partially Observable Mean Field Control for Artificial Collective Behavior](https://mlsanity.com/paper/2307.06175/) (2023)
- [Mean Field Type Control with Congestion (II): An Augmented Lagrangian Method](https://mlsanity.com/paper/1611.02023/) (2016)
- [On the system of partial differential equations arising in mean field type control](https://mlsanity.com/paper/1503.05044/) (2015)
- [Deep Learning for Population-Dependent Controls in Mean Field Control Problems with Common Noise](https://mlsanity.com/paper/2306.04788/) (2023)
- [A Class of Finite-Dimensional Numerically Solvable McKean-Vlasov Control Problems](https://mlsanity.com/paper/1803.00445/) (2018)
- [From finite population optimal stopping to mean field optimal stopping](https://mlsanity.com/paper/2210.16004/) (2022)
- [Optimal stopping of conditional McKean-Vlasov jump diffusions](https://mlsanity.com/paper/2207.13994/) (2022)
- [On the limit theory of mean field optimal stopping with non-Markov dynamics and common noise](https://mlsanity.com/paper/2310.00407/) (2023)
- [Time-inconsistent mean-field stopping problems: A regularized equilibrium approach](https://mlsanity.com/paper/2311.00381/) (2023)

## Built on by (most cited first, 1 of 1)

- [Deep Learning for the Multiple Optimal Stopping Problem](https://mlsanity.com/paper/2512.22961/) (2025)

## Abstract (arXiv)

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.