Convex neural network synthesis for robustness in the 1-norm

TL;DR

This paper introduces a convex optimization method to generate neural networks that are certifiably more robust, specifically targeting the robustness/accuracy trade-off in safety-critical control systems.

Contribution

It presents a fully convex semi-definite programming approach to synthesize neural networks with enhanced robustness in the 1-norm, applicable to model predictive control.

Findings

Method produces neural networks with improved robustness guarantees.

Application to model predictive control demonstrates practical effectiveness.

Balances robustness and accuracy in safety-critical systems.

Abstract

With neural networks being used to control safety-critical systems, they increasingly have to be both accurate (in the sense of matching inputs to outputs) and robust. However, these two properties are often at odds with each other and a trade-off has to be navigated. To address this issue, this paper proposes a method to generate an approximation of a neural network which is certifiably more robust. Crucially, the method is fully convex and posed as a semi-definite programme. An application to robustifying model predictive control is used to demonstrate the results. The aim of this work is to introduce a method to navigate the neural network robustness/accuracy trade-off.