# Continuous-time Optimal Stopping through Deep Reinforcement Learning

arXiv: https://arxiv.org/abs/2606.17545 · HTML: https://mlsanity.com/paper/2606.17545/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 16 of its 38 references that are in the map.
- First posted on arXiv 16 Jun 2026.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 16 of 16)

- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Optimal Stopping via Randomized Neural Networks](https://mlsanity.com/paper/2104.13669/) (2021)
- [Solving high-dimensional optimal stopping problems using deep learning](https://mlsanity.com/paper/1908.01602/) (2019)
- [Deep Neural Network Framework Based on Backward Stochastic Differential Equations for Pricing and Hedging American Options in High Dimensions](https://mlsanity.com/paper/1909.11532/) (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)
- [Learning to Optimally Stop Diffusion Processes, with Financial Applications](https://mlsanity.com/paper/2408.09242/) (2024)
- [Deep Learning for Ranking Response Surfaces with Applications to Optimal Stopping Problems](https://mlsanity.com/paper/1901.03478/) (2019)
- [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)
- [Adaptive Batching for Gaussian Process Surrogates with Application in Noisy Level Set Estimation](https://mlsanity.com/paper/2003.08579/) (2020)
- [mlOSP: Towards a Unified Implementation of Regression Monte Carlo Algorithms](https://mlsanity.com/paper/2012.00729/) (2020)
- [Deep Learning for the Multiple Optimal Stopping Problem](https://mlsanity.com/paper/2512.22961/) (2025)

## Abstract (arXiv)

Simulation based solvers for optimal stopping problems must discretize the stopping decision. Under classical dynamic programming, a coarse exercise grid with only a few stopping opportunities can materially undervalue the optimal expected reward, whereas on a very fine grid, approximation errors accumulate through the backward recursion. To remove this limitation, we develop a new reinforcement-learning inspired algorithm that enables us to learn the exercise rule at arbitrarily fine time resolution. Our CARLOS (Continuous-time Adaptive Reinforcement Learning for Optimal Stopping) algorithm utilizes an aggregate deep neural network (ADNN) to learn a joint space-time decision boundary. Starting from a coarse time grid, we progressively increase the frequency of stopping opportunities, while in parallel training the ADNN to refine its timing-value estimates. We moreover design an adaptive sampling strategy that gradually concentrates training effort near the stopping boundary. Benchmarked results show that CARLOS delivers higher prices than existing Bermudan solvers, approaching the American upper bound, and achieves high computational efficiency relative to non-RL comparators.