# Kernel-Based Optimal Control: An Infinitesimal Generator Approach

arXiv: https://arxiv.org/abs/2412.01591 · HTML: https://mlsanity.com/paper/2412.01591/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 59 references that are in the map.
- First posted on arXiv 2 Dec 2024.

## Builds on (most cited first, 23 of 23)

- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Data-driven approximation of the Koopman generator: Model reduction, system identification, and control](https://mlsanity.com/paper/1909.10638/) (2019)
- [Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2205.14027/) (2022)
- [Optimal Rates for Regularized Conditional Mean Embedding Learning](https://mlsanity.com/paper/2208.01711/) (2022)
- [Koopman Operator Dynamical Models: Learning, Analysis and Control](https://mlsanity.com/paper/2102.02522/) (2021)
- [Sharp Spectral Rates for Koopman Operator Learning](https://mlsanity.com/paper/2302.02004/) (2023)
- [Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem](https://mlsanity.com/paper/2211.08875/) (2022)
- [Finite-data error bounds for Koopman-based prediction and control](https://mlsanity.com/paper/2108.07102/) (2021)
- [Lyapunov-stable Neural Control for State and Output Feedback: A Novel Formulation](https://mlsanity.com/paper/2404.07956/) (2024)
- [Koopman Kernel Regression](https://mlsanity.com/paper/2305.16215/) (2023)
- [Nonparametric approximation of conditional expectation operators](https://mlsanity.com/paper/2012.12917/) (2020)
- [Physics-Informed Neural Network Policy Iteration: Algorithms, Convergence, and Verification](https://mlsanity.com/paper/2402.10119/) (2024)
- [Consistent Long-Term Forecasting of Ergodic Dynamical Systems](https://mlsanity.com/paper/2312.13426/) (2023)
- [Learning the Infinitesimal Generator of Stochastic Diffusion Processes](https://mlsanity.com/paper/2405.12940/) (2024)
- [HJB Optimal Feedback Control with Deep Differential Value Functions and Action Constraints](https://mlsanity.com/paper/1909.06153/) (2019)
- [Nonparametric Control Koopman Operators](https://mlsanity.com/paper/2405.07312/) (2024)
- [Continuous-Time Fitted Value Iteration for Robust Policies](https://mlsanity.com/paper/2110.01954/) (2021)
- [Data-Driven Chance Constrained Control using Kernel Distribution Embeddings](https://mlsanity.com/paper/2202.04193/) (2022)
- [Towards Global Optimal Control via Koopman Lifts](https://mlsanity.com/paper/2003.01265/) (2020)
- [Convex operator-theoretic methods in stochastic control](https://mlsanity.com/paper/2305.17628/) (2023)
- [Solving Chance Constrained Optimization under Non-Parametric Uncertainty Through Hilbert Space Embedding](https://mlsanity.com/paper/1811.09311/) (2018)
- [Controlled density transport using Perron Frobenius generators](https://mlsanity.com/paper/2304.13829/) (2023)
- [Data-Driven Stochastic Optimal Control in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2407.16407/) (2024)

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

- [Koopman operator theory: fundamentals, control, and applications](https://mlsanity.com/paper/2607.01819/) (2026)

## Abstract (arXiv)

This paper presents a novel operator-theoretic approach for optimal control of nonlinear stochastic systems within reproducing kernel Hilbert spaces. Our learning framework leverages data samples of system dynamics and stage cost functions, with only control penalties and constraints provided. The proposed method directly learns the infinitesimal generator of a controlled stochastic diffusion in an infinite-dimensional hypothesis space. We demonstrate that our approach seamlessly integrates with modern convex operator-theoretic Hamilton-Jacobi-Bellman recursions, enabling a data-driven solution to the optimal control problems. Furthermore, our learning framework includes nonparametric estimators for uncontrolled infinitesimal generators as a special case. Numerical experiments, ranging from synthetic differential equations to simulated robotic systems, showcase the advantages of our approach compared to both modern data-driven and classical nonlinear programming methods for optimal control.