Convex neural network synthesis for robustness in the 1-norm
Ross Drummond, Chris Guiver, Matthew C. Turner
TL;DR
This work tackles the robustness–accuracy trade-off in neural networks for safety-critical control by proposing a fully convex neural network synthesis method. By reformulating robustness in the $\ell_1$-norm and exploiting ReLU representations, the authors derive an SDP (single, convex optimization) to compute a robustified network that remains close to the original mapping. The key contribution is a tractable, LMI-based framework that certifiably improves robustness while controlling similarity to the original network, enabling certifiable performance in applications such as robust MPC. The approach provides a practical pathway to integrate neural networks into safety-critical controllers with tunable robustness guarantees and potential for scalable controller synthesis.
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.