Collaborative Research: Distributed Bilevel Optimization in Multi-Agent Systems

二层优化是一个发展迅速的研究领域，在机器学习、信号处理、通信、最优控制、能源和电力系统等领域都有重要的应用。然而，已有的BO研究大多集中在单智能体系统中的算法上，而现代电力系统、通信、能源等领域的应用往往需要解决多智能体分布式网络中的问题。该项目旨在缩小这一差距。具体地说，在这个项目中，我们将设计新的算法来解决分散和联邦环境下的多智能体系统上的BO。将建立所提出的算法的收敛，为它们提供理论基础。这些算法将在具有用户友好界面的计算机代码中实现，并将公开提供，以便其他领域的研究人员使用。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推力：分散式BO、联邦BO和具有共识约束的分布式BO。对于分散的BO，我们将研究当下层问题存在唯一解时的分散单环一阶算法，以及当下层问题允许多解时的基于分散值函数的方法。我们还将研究不同的方法来加速分布式BO的算法。对于联邦BO，我们将设计算法来实现对异质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能力，如不同的存储能力和计算能力。最后，我们研究了具有显式一致性约束的BO的分布式算法。由于约束是线性方程，我们计划研究乘子交替方向法(ADMM)来解决这个问题。具体地说，我们将研究多智能体系统中分布式随机BO的分散ADMM和联邦ADMM的可能性。此外，我们将研究分布式BO在无线通信网络的功率控制和超参数学习中的新应用。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.