# Sparse optimal stochastic control

arXiv: https://arxiv.org/abs/2109.07716 · HTML: https://mlsanity.com/paper/2109.07716/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2021.

## Built on by (most cited first, 2 of 2)

- [Kullback-Leibler control for discrete-time nonlinear systems on continuous spaces](https://mlsanity.com/paper/2203.12864/) (2022)
- [Tsallis Entropy Regularization for Linear Quadratic Regulator and Kullback-Leibler Control](https://mlsanity.com/paper/2403.01805/) (2024)

## Abstract (arXiv)

In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the L0 cost functional, in general, the value function is not differentiable in the domain. Then, we characterize the value function as a viscosity solution to the associated Hamilton-Jacobi-Bellman (HJB) equation. Based on the result, we derive a necessary and sufficient condition for the L0 optimality, which immediately gives the optimal feedback map. Especially for control-affine systems, we consider the relationship with L1 optimal control problem and show an equivalence theorem.