Data-Driven Distributed Optimization via Aggregative Tracking and Deep-Learning

In this paper, we propose a novel distributed data-driven optimization scheme. In detail, we focus on the so-called aggregative framework, a scenario in which a set of agents aim to cooperatively minimize the sum of local costs, each depending on both local decision variables and an aggregation of all of them. We consider a data-driven setup where each objective function is unknown and can be sampled at a single point per iteration (thanks to, e.g., feedback from users or sensors). We address this scenario through a distributed algorithm combining three components: (i) a learning part leveraging neural networks to learn the local costs descent direction, (ii) an optimization routine steering the estimates according to the learned direction to minimize the global cost, and (iii) a tracking mechanism locally reconstructing the unavailable global quantities. Using tools from system theory, i.e., timescale separation and averaging theory, we formally prove that in strongly convex setups, the distributed scheme linearly converges to a neighborhood of the optimum, whose radius depends on the accuracy of the neural networks. Finally, numerical simulations validate the theoretical results.