Master Degree Project Presentation: "Learning Distributed Optimization with Graph Neural Networks"

Abstract: The emergence of large networked systems, where the agents typically have access only to local private information, together with the explosion in data dimensionality, has necessitated the development of efficient algorithms for distributed optimization. The Alternating Direction Method of Multipliers (ADMM) is well suited for this task, as it can be implemented in a distributed form, relying on decentralized communication between the agents. Still, the need and possibility for acceleration remain, especially when adapting the algorithm to certain problem classes. Learning-to-Optimize (L2O) has the potential to automate this process by leveraging machine learning methods. In this context, Graph Neural Networks (GNNs) seem to be a natural choice as they are able to learn and reason about graph-structured data, thereby outperforming traditional neural network architectures.

Thus, this thesis will explore the abilities of GNNs to enhance the performance of distributed ADMM, with a specific focus on how GNNs operate. It will adopt a model-based L2O approach that allows the GNN to influence certain components of the algorithm, while crucially preserving its convergence property. In particular, we propose two architectures for pivotal parts of ADMM, namely the step size and the local optimization step, that can be transferred to other graph algorithms. With experiments, we will finally provide first insights into how much these strategies can improve ADMM on unseen problems of the same class.