# Data-driven optimal stopping: A pure exploration analysis

arXiv: https://arxiv.org/abs/2312.05880 · HTML: https://mlsanity.com/paper/2312.05880/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 26 references that are in the map.
- First posted on arXiv 10 Dec 2023.

## Builds on (most cited first, 7 of 7)

- [Optimal Best Arm Identification with Fixed Confidence](https://mlsanity.com/paper/1602.04589/) (2016)
- [Policy Gradient and Actor-Critic Learning in Continuous Time and Space: Theory and Algorithms](https://mlsanity.com/paper/2111.11232/) (2021)
- [Optimal Best-arm Identification in Linear Bandits](https://mlsanity.com/paper/2006.16073/) (2020)
- [Continuous-Time Model-Based Reinforcement Learning](https://mlsanity.com/paper/2102.04764/) (2021)
- [Exploration-exploitation trade-off for continuous-time episodic reinforcement learning with linear-convex models](https://mlsanity.com/paper/2112.10264/) (2021)
- [Learning to reflect: A unifying approach for data-driven stochastic control strategies](https://mlsanity.com/paper/2104.11496/) (2021)
- [Data-driven rules for multidimensional reflection problems](https://mlsanity.com/paper/2311.06639/) (2023)

## Built on by (most cited first, 4 of 4)

- [Exploratory Optimal Stopping: A Singular Control Formulation](https://mlsanity.com/paper/2408.09335/) (2024)
- [Learning to steer with Brownian noise](https://mlsanity.com/paper/2410.03221/) (2024)
- [Reinforcement Learning in Real Option Models](https://mlsanity.com/paper/2602.15643/) (2026)
- [Learning Optimal Search Strategies](https://mlsanity.com/paper/2603.02356/) (2026)

## Abstract (arXiv)

The standard theory of optimal stopping is based on the idealised assumption that the underlying process is essentially known. In this paper, we drop this restriction and study data-driven optimal stopping for a general diffusion process, focusing on investigating the statistical performance of the proposed estimator of the optimal stopping barrier. More specifically, we derive non-asymptotic upper bounds on the simple regret, along with uniform and non-asymptotic PAC bounds. Minimax optimality is verified by completing the upper bound results with matching lower bounds on the simple regret. All results are shown both under general conditions on the payoff functions and under more refined assumptions that mimic the margin condition used in binary classification, leading to an improved rate of convergence. Additionally, we investigate how our results on the simple regret transfer to the cumulative regret for a specific exploration-exploitation strategy, both with respect to lower bounds and upper bounds.