# Efficient model-based reinforcement learning for approximate online optimal

arXiv: https://arxiv.org/abs/1502.02609 · HTML: https://mlsanity.com/paper/1502.02609/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2015.

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

- [Safe Exploration in Model-based Reinforcement Learning using Control Barrier Functions](https://mlsanity.com/paper/2104.08171/) (2021)
- [A Physics-Informed Learning Framework to Solve the Infinite-Horizon Optimal Control Problem](https://mlsanity.com/paper/2505.21842/) (2025)
- [Reinforcement learning in pursuit-evasion differential game: safety, stability and robustness](https://mlsanity.com/paper/2507.19516/) (2025)

## Abstract (arXiv)

In this paper the infinite horizon optimal regulation problem is solved online for a deterministic control-affine nonlinear dynamical system using the state following (StaF) kernel method to approximate the value function. Unlike traditional methods that aim to approximate a function over a large compact set, the StaF kernel method aims to approximate a function in a small neighborhood of a state that travels within a compact set. Simulation results demonstrate that stability and approximate optimality of the control system can be achieved with significantly fewer basis functions than may be required for global approximation methods.