# Deep Learning for the Multiple Optimal Stopping Problem

arXiv: https://arxiv.org/abs/2512.22961 · HTML: https://mlsanity.com/paper/2512.22961/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 38 references that are in the map.
- First posted on arXiv 28 Dec 2025.

## Builds on (most cited first, 17 of 17)

- [Optimal Stopping via Randomized Neural Networks](https://mlsanity.com/paper/2104.13669/) (2021)
- [Deep neural networks algorithms for stochastic control problems on finite horizon: convergence analysis](https://mlsanity.com/paper/1812.04300/) (2018)
- [Solving high-dimensional optimal stopping problems using deep learning](https://mlsanity.com/paper/1908.01602/) (2019)
- [Convergence of the Backward Deep BSDE Method with Applications to Optimal Stopping Problems](https://mlsanity.com/paper/2210.04118/) (2022)
- [Deep neural network expressivity for optimal stopping problems](https://mlsanity.com/paper/2210.10443/) (2022)
- [Deep Learning for Ranking Response Surfaces with Applications to Optimal Stopping Problems](https://mlsanity.com/paper/1901.03478/) (2019)
- [Randomized optimal stopping algorithms and their convergence analysis](https://mlsanity.com/paper/2002.00816/) (2020)
- [Deep Reinforcement Learning for Optimal Stopping with Application in Financial Engineering](https://mlsanity.com/paper/2105.08877/) (2021)
- [A deep primal-dual BSDE method for optimal stopping problems](https://mlsanity.com/paper/2409.06937/) (2024)
- [Solving optimal stopping problems with Deep Q-Learning](https://mlsanity.com/paper/2101.09682/) (2021)
- [Solving the optimal stopping problem with reinforcement learning: an application in financial option exercise](https://mlsanity.com/paper/2208.00765/) (2022)
- [Simultaneous upper and lower bounds of American-style option prices with hedging via neural networks](https://mlsanity.com/paper/2302.12439/) (2023)
- [Deep Neural Operator Learning for Probabilistic Models](https://mlsanity.com/paper/2511.07235/) (2025)
- [Optimal Stopping with Gaussian Processes](https://mlsanity.com/paper/2209.14738/) (2022)
- [From finite population optimal stopping to mean field optimal stopping](https://mlsanity.com/paper/2210.16004/) (2022)
- [Learning to Stop: Deep Learning for Mean Field Optimal Stopping](https://mlsanity.com/paper/2410.08850/) (2024)
- [The non-linear multiple stopping problem: between the discrete and the continuous time](https://mlsanity.com/paper/2504.13503/) (2025)

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

- [Continuous-time Optimal Stopping through Deep Reinforcement Learning](https://mlsanity.com/paper/2606.17545/) (2026)

## Abstract (arXiv)

This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex recursive dependencies that remain challenging. We address this by combining the Dynamic Programming Principle with neural network approximation of the value function. Unlike policy-search methods, our algorithm explicitly learns the value surface. We first consider the discrete-time problem and analyze neural network training error. We then turn to continuous problems and analyze the additional error due to the discretization of the underlying stochastic processes. Numerical experiments on high-dimensional American basket options and nonlinear utility maximization demonstrate that our method provides an efficient and scalable method for the multiple optimal stopping problem.