# A computationally lightweight safe learning algorithm

arXiv: https://arxiv.org/abs/2309.03672 · HTML: https://mlsanity.com/paper/2309.03672/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 23 references that are in the map.
- First posted on arXiv 7 Sep 2023.

## Builds on (most cited first, 10 of 10)

- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Benchmarking Deep Reinforcement Learning for Continuous Control](https://mlsanity.com/paper/1604.06778/) (2016)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Stagewise Safe Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1806.07555/) (2018)
- [GoSafe: Globally Optimal Safe Robot Learning](https://mlsanity.com/paper/2105.13281/) (2021)
- [GoSafeOpt: Scalable Safe Exploration for Global Optimization of Dynamical Systems](https://mlsanity.com/paper/2201.09562/) (2022)
- [Certainty Equivalent Perception-Based Control](https://mlsanity.com/paper/2008.12332/) (2020)
- [Safe and Efficient Model-free Adaptive Control via Bayesian Optimization](https://mlsanity.com/paper/2101.07825/) (2021)
- [Decentralized diffusion-based learning under non-parametric limited prior knowledge](https://mlsanity.com/paper/2305.03295/) (2023)

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

- [Safety and optimality in learning-based control at low computational cost](https://mlsanity.com/paper/2505.08026/) (2025)
- [Computationally lightweight classifiers with frequentist bounds on predictions](https://mlsanity.com/paper/2603.22128/) (2026)
- [Computationally efficient safe exploration in reinforcement learning](https://mlsanity.com/paper/2609.22919/) (2026)

## Abstract (arXiv)

Safety is an essential asset when learning control policies for physical systems, as violating safety constraints during training can lead to expensive hardware damage. In response to this need, the field of safe learning has emerged with algorithms that can provide probabilistic safety guarantees without knowledge of the underlying system dynamics. Those algorithms often rely on Gaussian process inference. Unfortunately, Gaussian process inference scales cubically with the number of data points, limiting applicability to high-dimensional and embedded systems. In this paper, we propose a safe learning algorithm that provides probabilistic safety guarantees but leverages the Nadaraya-Watson estimator instead of Gaussian processes. For the Nadaraya-Watson estimator, we can reach logarithmic scaling with the number of data points. We provide theoretical guarantees for the estimates, embed them into a safe learning algorithm, and show numerical experiments on a simulated seven-degrees-of-freedom robot manipulator.