# Safe Approximate Dynamic Programming Via Kernelized Lipschitz Estimation

arXiv: https://arxiv.org/abs/1907.02151 · HTML: https://mlsanity.com/paper/1907.02151/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2019.

## Built on by (most cited first, 4 of 4)

- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Chordal Sparsity for Lipschitz Constant Estimation of Deep Neural Networks](https://mlsanity.com/paper/2204.00846/) (2022)
- [A Physics-Informed Machine Learning Framework for Safe and Optimal Control of Autonomous Systems](https://mlsanity.com/paper/2502.11057/) (2025)
- [Formal Verification of Unknown Dynamical Systems via Gaussian Process Regression](https://mlsanity.com/paper/2201.00655/) (2021)

## Abstract (arXiv)

We develop a method for obtaining safe initial policies for reinforcement learning via approximate dynamic programming (ADP) techniques for uncertain systems evolving with discrete-time dynamics. We employ kernelized Lipschitz estimation and semidefinite programming for computing admissible initial control policies with provably high probability. Such admissible controllers enable safe initialization and constraint enforcement while providing exponential stability of the equilibrium of the closed-loop system.