# Deep Reinforcement Learning in Finite-Horizon to Explore the Most Probable Transition Pathway

arXiv: https://arxiv.org/abs/2304.12994 · HTML: https://mlsanity.com/paper/2304.12994/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2023.

## Built on by (most cited first, 5 of 5)

- [Early Warning Prediction with Automatic Labeling in Epilepsy Patients](https://mlsanity.com/paper/2310.06059/) (2023)
- [Estimating Reaction Barriers with Deep Reinforcement Learning](https://mlsanity.com/paper/2407.12453/) (2024)
- [Computing Transition Pathways for the Study of Rare Events Using Deep Reinforcement Learning](https://mlsanity.com/paper/2404.05905/) (2024)
- [Early warning prediction: Onsager-Machlup vs Schr"odinger](https://mlsanity.com/paper/2602.00143/) (2026)
- [Chess on Ice: Curling Tactical Decision-Making via Backward Induction and Deep Reinforcement Learning](https://mlsanity.com/paper/2608.02379/) (2026)

## Abstract (arXiv)

In many scientific and engineering problems, noise and nonlinearity are unavoidable, which could induce interesting mathematical problem such as transition phenomena. This paper focuses on efficiently discovering the most probable transition pathway for stochastic dynamical systems employing reinforcement learning. With the Onsager-Machlup action functional theory to quantify rare events in stochastic dynamical systems, finding the most probable pathway is equivalent to solving a variational problem on the action functional. When the action function cannot be explicitly expressed by paths near the reference orbit, the variational problem needs to be converted into an optimal control problem. First, by integrating terminal prediction into the reinforcement learning framework, we develop a Terminal Prediction Deep Deterministic Policy Gradient (TP-DDPG) algorithm to deal with the finite-horizon optimal control issue in a forward way. Next, we present the convergence analysis of our algorithm for the value function in terms of the neural network's approximation error and estimation error. Finally, we conduct various experiments in different dimensions for the transition problems in applications to illustrate the effectiveness of our algorithm.