Collaborative Research: Distributed Bilevel Optimization in Multi-Agent Systems

协作研究：多智能体系统中的分布式双层优化

• 批准号: 2326591
• 负责人: Shiqian Ma
• 金额: $ 25万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-15 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2326591&HistoricalAwards=false
• 关键词: Collaborative; Research; Distributed; Bilevel; Optimization

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.

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、能源到电力系统等不同领域都有许多重要的应用。然而，现有的BO研究大多集中在单智能体系统的算法上，而电力系统、通信和能源等现代应用往往需要在多智能体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去中心化和联合设置中多代理系统上的 BO。将建立所提出算法的收敛性，为其提供理论基础。这些算法将以具有用户友好界面的计算机代码来实现，该界面将公开，以便其他领域的研究人员可以使用。该项目的成果预计将为解决电力系统、最优控制和通信网络等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。该项目由三大主旨组成：去中心化 BO、联邦 BO 和具有共识约束的分布式 BO。对于去中心化BO，当低层问题有唯一解时，我们将研究去中心化的单循环一阶算法；当低层问题有多个解时，我们将研究基于价值函数的去中心化方法。我们还将研究加速去中心化 BO 算法的不同方法。对于联邦BO，我们将设计能够针对异构数据问题实现线性加速的算法。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（例如不同的存储容量和计算能力）造成的。在最后一个主旨中，我们研究了具有明确共识约束的 BO 分布式算法。由于约束是线性等式，我们计划研究乘子交替方向法（ADMM）来解决这个问题。具体来说，我们将研究去中心化 ADMM 和联邦 ADMM 在多智能体系统中用于分布式随机 BO 的可能性。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中的新应用。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。