Optimising (Graph) Neural Networks Using Exact Solvers
Speaker: Neil Yorke-Smith
Abstract: Convolutional neural networks have been modelled as constraints in mixed integer linear programming (MILP) mathematical optimisation models, enabling surrogate-based optimisation in various domains and efficient solution of machine learning certification problems. However, previous mathematical formulations of neural networks have been mostly limited to multi-layer perceptrons. Graph neural networks (GNNs) can learn from non-euclidean data structures such as molecular structures efficiently. We propose a bilinear formulation for ReLU graph convolutional neural networks and a MILP formulation for ReLU GraphSAGE models, both novel at the time of their development. These formulations enable solving optimisation problems with trained GNNs embedded to global optimality. We further propose a nonlinear formulation for transformer neural networks. The value of these mathematical formulations are demonstrated in multiple chemical engineering scenarios. This work is joint with Sian Hallsworth, Tanuj Karia, Tom McDonald, Artur Schweidtmann and Calvin Tsay.
Bio: Neil Yorke-Smith directs the Socio-Technical Algorithmic Research (STAR) Lab at TU Delft. His research addresses a fundamental question of the AI era: how can technology help people make decisions in complex socio-technical situations? Yorke-Smith is an Associate Professor in the Faculty of Electrical Engineering, Mathematics and Computer Science. He is a Fellow of the TRAIL Research School, a Senior Member of AAAI, a Senior Member of ACM, and a member of CAIRNE and ELLIS. In addition to directing the STAR Lab, Yorke-Smith co-directs the ICAI AI & Logistics Lab (AILogLab). Website: starlab.ewi.tudelft.nl