Continuous-time Optimal Stopping through Deep Reinforcement Learning
On the map: Deep reinforcement learning methods → RL theory and sample complexity
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.
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.
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16 of 38 references.
References · 16
- 2017DGM: A deep learning algorithm for solving partial differential equationscited by 678
- 2021Optimal Stopping via Randomized Neural Networkscited by 28
- 2019Solving high-dimensional optimal stopping problems using deep learningcited by 22
- 2019Deep Neural Network Framework Based on Backward Stochastic Differential Equations for Pricing and Hedging American Options in High Dimensionscited by 14
- 2022Convergence of the Backward Deep BSDE Method with Applications to Optimal Stopping Problemscited by 9
- 2022Deep neural network expressivity for optimal stopping problemscited by 9
- 2024Learning to Optimally Stop Diffusion Processes, with Financial Applicationscited by 9
- 2019Deep Learning for Ranking Response Surfaces with Applications to Optimal Stopping Problemscited by 8
- 2021Deep Reinforcement Learning for Optimal Stopping with Application in Financial Engineeringcited by 6
- 2024A deep primal-dual BSDE method for optimal stopping problemscited by 4
- 2021Solving optimal stopping problems with Deep Q-Learningcited by 3
- 2022Solving the optimal stopping problem with reinforcement learning: an application in financial option exercisecited by 3
4 more
- 2023Simultaneous upper and lower bounds of American-style option prices with hedging via neural networkscited by 3
- 2020Adaptive Batching for Gaussian Process Surrogates with Application in Noisy Level Set Estimationcited by 2
- 2020mlOSP: Towards a Unified Implementation of Regression Monte Carlo Algorithmscited by 1
- 2025Deep Learning for the Multiple Optimal Stopping Problemcited by 1
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- 2024Efficient Exploration in Deep Reinforcement Learning: A Novel Bayesian Actor-Critic Algorithm
- 2024Deep Reinforcement Learning: A Convex Optimization Approach
- 2025Stabilizing Reinforcement Learning with LLMs: Formulation and Practices
- 2024Deep Reinforcement Learning for Dynamic Algorithm Selection: A Proof-of-Principle Study on Differential Evolution
- 2025A Practical Introduction to Deep Reinforcement Learning
- 2021Learning Algorithms for Regenerative Stopping Problems with Applications to Shipping Consolidation in Logistics