Collaborative Research: Distributed Bilevel Optimization in Multi-Agent Systems

Bilevel optimization (BO) is a fast growing research area that finds many important applications in different fields ranging from machine learning, signal processing, communication, optimal control, energy to power systems. However, most existing research on BO has been focusing on algorithms in single-agent system, while the modern applications in power system, communication and energy often require the problems to be solved in multi-agent distributed networks. This project aims to close this gap. Specifically, in this project, we will design new algorithms for solving BO over multi agent system in decentralized and federated settings. Convergence of the proposed algorithms will be established to provide theoretical foundations for them. The algorithms will be implemented in computer codes with user-friendly interface which will be made publicly available so that they can be used by researchers from other fields. The outcomes of this project are expected to provide new tools for solving challenging distributed BO problems in multi-agent systems arising from power systems, optimal control and communication networks, which will also benefit researchers from academia, government labs and industry. This project consists of three major thrusts: decentralized BO, federated BO, and distributed BO with consensus constraints. For decentralized BO, we will study decentralized single-loop first-order algorithms when the lower-level problem admits unique solution, and decentralized value-function-based methods when the lower-level problem admits multiple solutions. We will also study different ways to accelerate algorithms for decentralized BO. For federated BO, we will design algorithms that can achieve linear speedup for problems with heterogeneous data. We will also study strategies to improve the resilience of federated BO to system-level heterogeneity, which is due to different system capabilities such as varying storage capacities and computing power. In the last thrust, we study distributed algorithms for BO with explicit consensus constraints. Since the constraints are linear equalities, we plan to study the alternating direction method of multipliers (ADMM) for solving this problem. Specifically, we will investigate the possibilities of decentralized ADMM and federated ADMM for distributed stochastic BO in multi-agent systems. Moreover, we will study new applications of distributed BO in power control and hyperparameter learning in wireless communication networks. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.