Collaborative Research: Distributed Bilevel Optimization in Multi-Agent Systems

双层优化（BO）是一个快速发展的研究领域，在机器学习、信号处理、通信、最优控制、能源和电力系统等不同领域有许多重要的应用。然而，现有的BO研究大多集中在单Agent系统中的算法，而现代电力系统、通信和能源等领域的应用往往需要在多Agent分布式网络中解决问题。该项目旨在缩小这一差距。具体来说，在这个项目中，我们将设计新的算法来解决BO多代理系统在分散和联邦设置。并证明了算法的收敛性，为算法的实现提供了理论依据.这些算法将以具有用户友好界面的计算机代码实现，这些代码将公开提供，以便其他领域的研究人员可以使用。该项目的成果有望为解决电力系统、最优控制和通信网络中多智能体系统中具有挑战性的分布式BO问题提供新的工具，这也将使学术界、政府实验室和工业界的研究人员受益。该项目包括三个主要目标：去中心化BO、联邦BO和带有共识约束的分布式BO。对于分散BO，我们将研究分散单循环一阶算法时，低层问题承认唯一的解决方案，和分散的价值函数为基础的方法时，低层问题承认多个解决方案。我们还将研究加速分散BO算法的不同方法。对于联邦BO，我们将设计算法来实现异构数据问题的线性加速。我们还将研究提高联邦BO对系统级异构性的弹性的策略，这是由于不同的系统功能，如不同的存储容量和计算能力。在最后的推力，我们研究了分布式算法BO明确的共识约束。由于约束条件是线性等式，我们计划研究交替方向乘子法（ADMM）解决这个问题。具体来说，我们将调查的可能性，分散ADMM和联邦ADMM的分布式随机BO多智能体系统。此外，我们将研究分布式BO在无线通信网络中的功率控制和超参数学习方面的新应用。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.