# Deterministic control of randomly-terminated processes

arXiv: https://arxiv.org/abs/1310.7161 · HTML: https://mlsanity.com/paper/1310.7161/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2013.

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

- [Surveillance Evasion Through Bayesian Reinforcement Learning](https://mlsanity.com/paper/2109.14811/) (2021)

## Abstract (arXiv)

We consider both discrete and continuous "uncertain horizon" deterministic control processes, for which the termination time is a random variable. We examine the dynamic programming equations for the value function of such processes, explore their connections to infinite-horizon and optimal-stopping problems, and derive sufficient conditions for the applicability of non-iterative (label-setting) methods. In the continuous case, the resulting PDE has a free boundary, on which all characteristic curves originate. The causal properties of "uncertain horizon" problems can be exploited to design efficient numerical algorithms: we derive causal semi-Lagrangian and Eulerian discretizations for the isotropic randomly-terminated problems, and use them to build a modified version of the Fast Marching Method. We illustrate our approach using numerical examples from optimal idle-time processing and expected response-time minimization.