# Convex operator-theoretic methods in stochastic control

arXiv: https://arxiv.org/abs/2305.17628 · HTML: https://mlsanity.com/paper/2305.17628/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2023.

## Built on by (most cited first, 3 of 3)

- [Nonparametric Control Koopman Operators](https://mlsanity.com/paper/2405.07312/) (2024)
- [Data-Driven Stochastic Optimal Control in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2407.16407/) (2024)
- [Kernel-Based Optimal Control: An Infinitesimal Generator Approach](https://mlsanity.com/paper/2412.01591/) (2024)

## Abstract (arXiv)

This paper is about operator-theoretic methods for solving nonlinear stochastic optimal control problems to global optimality. These methods leverage on the convex duality between optimally controlled diffusion processes and Hamilton-Jacobi-Bellman (HJB) equations for nonlinear systems in an ergodic Hilbert-Sobolev space. In detail, a generalized Bakry-Emery condition is introduced under which one can establish the global exponential stabilizability of a large class of nonlinear systems. It is shown that this condition is sufficient to ensure the existence of solutions of the ergodic HJB for stochastic optimal control problems on infinite time horizons. Moreover, a novel dynamic programming recursion for bounded linear operators is introduced, which can be used to numerically solve HJB equations by a Galerkin projection.