A computationally lightweight safe learning algorithm

TL;DR

This paper introduces a computationally efficient safe learning algorithm for control policies that uses the Nadaraya-Watson estimator, enabling probabilistic safety guarantees with better scalability than Gaussian processes.

Contribution

It replaces Gaussian process inference with the Nadaraya-Watson estimator in safe learning, achieving logarithmic scaling with data points and maintaining safety guarantees.

Findings

Logarithmic scaling with data points for the estimator

Theoretical safety guarantees provided

Successful numerical experiments on a robot manipulator

Abstract

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.