CAREER: Advancing Mathematical Models and Algorithms for Decentralized Optimization in Complex Multi-agent Networks

人工智能和无线传感器技术的最新进展导致了合作优化方面的重大研究。在该机制中，多个代理(例如，处理器或传感器)在本地与其邻居通信它们的信息，以协作地优化全局性能度量。这种分散的范例在与集中式协调器通信不受欢迎或不可能的网络域中扮演着关键角色。这也允许保护代理的隐私。正是由于这些原因，分散优化方法的设计和性能分析在数据科学、无线网络和通信网络等应用领域引起了越来越多的关注。该项目旨在开发新的模型、数学工具和计算算法，以解决新兴的复杂多智能体系统。这种复杂性出现在新兴的应用中，如遥感、可再生能源的经济调度模型和交通网络中的效率估计。该项目有可能大大缩小复杂多代理网络的理论和现实世界实践之间的差距。此外，与行业合作伙伴的合作将促进有效的知识转移。该项目还旨在通过几项全面整合的教育和外展活动，提高高中生、教育工作者和大学生的认识和兴趣。这些措施包括加强斯蒂尔沃特高中教师的专业发展，让中学生参与课外活动，以及通过让代表性不足的本科生参与研究来促进多样性。在新兴的复杂多智能体网络中，提出分布式约束优化的计算模型和算法是一个长期的研究目标。为了追求这一目标，学院早期职业发展(CALEAR)基金的研究目标是应用分布式优化领域的变分不等式和正则化理论来设计新的算法，该算法具有可证明的性能保证，可以处理具有复杂约束的多代理网络。这种复杂性出现在无线传感器网络、交通网络和机器学习等应用领域，在这些领域中，由于以下因素的存在，优化模型变得复杂：(1)约束的不确定性和非线性；(2)内部大规模优化问题；(3)均衡约束。最先进的方法包括加权平均共识法、推和法和交替方向乘子法，通常是在函数约束易于规划的前提下工作的。这些方案在很大程度上依赖于拉格朗日对偶理论，不会导致异步协议和通信延迟。因此，这项研究有望通过以下方式推进复杂网络上的分布式优化领域：(I)利用变分不等式理论开发一个增强的数学建模框架；(Ii)设计和分析一类新的迭代正则化的基于共识的算法，以解决建模框架中的明确性能界限；以及(Iii)探索解决建模框架中的非光滑性的新方法。长期教育目标是扩大K-12和大学生(特别是妇女和在STEM中代表性不足的少数群体)在运筹学和应用数学领域的参与。为了追求这一目标，这个职业项目的教育目标是激励和吸引年轻人、正规和非正规教育工作者、本科生和研究生理解优化在未来实践中的作用。这包括以下活动：(1)为中学教师提供为期四周的专业发展讲习班；(2)为斯蒂尔沃特高中学生制定课后STEM方案；(3)与俄克拉荷马州路易斯·斯托克斯少数群体参与联盟合作，让代表不足的本科生参与国际和平协会的研究；开发本科和高级博士课程。该项目由能源、电力、控制和网络计划(EPCN)、既定的激励竞争研究计划(EPSCoR)和运营工程计划(OE)联合资助。该奖项反映了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。

The recent advances in artificial intelligence and wireless sensor technologies have led to significant research in cooperative optimization. In this regime, multiple agents (e.g., processors or sensors) communicate their information locally with their neighbors to cooperatively optimize a global performance metric. This decentralized paradigm plays a key role in the network domains where communication with a centralized coordinator is either undesirable or impossible. This also allows for preserving the privacy of the agents. It is for these reasons that the design and performance analysis of decentralized optimization methods have attracted a growing attention in several application domains such as data science, wireless networks, and communication networks. This project is aimed at development of new models, mathematical tools, and computational algorithms to address emerging complex multi-agent systems. This complexity arises in emerging applications such as remote sensing, economic dispatch models with renewable energy, and efficiency estimation in transportation networks. This project has the potential to substantially reduce the gap between the theory and real-world practice of complex multi-agent networks. Moreover, collaborations with the industrial partner will facilitate effective knowledge transfer. This project is also aimed at increasing awareness and interest among high school students, educators, and college students through several fully integrated educational and outreach activities. These include enhancing professional development of teachers of Stillwater High School, engaging secondary students in after school activities, and promoting diversity through involvement of underrepresented undergraduate students in research. The long-term research goal is to advance the computational models and algorithms for distributed constrained optimization in emerging complex multi-agent networks. In pursuit of this goal, the research objective of this Faculty Early Career Development (CAREER) grant is to apply the theory of variational inequalities and regularization in the field of distributed optimization to design new algorithms with provable performance guarantees that can address multi-agent networks with complex constraints. This complexity arises in several application domains such as wireless sensor networks, transportation networks, and machine learning, where the optimization model is complicated due to the presence of: (1) uncertainty and nonlinearity in constraints; (2) an inner-level large-scale optimization problem; or (3) equilibrium constraints. The state-of-the-art approaches including weighted-averaging consensus, push-sum, and alternate direction multiplier methods work often under the premise that functional constraints are easy-to-project. These schemes rely significantly on Lagrangian duality theory and do not lend themselves to asynchronous protocols and communication delays. Accordingly, this research is expected to advance the area of distributed optimization over complex networks by: (i) Development of an enhanced mathematical modeling framework by utilizing the theory of variational inequalities; (ii) Design and analysis of new classes of iteratively regularized consensus-based algorithms with explicit performance bounds to address the modeling framework; and (iii) Explore novel ways to address nonsmoothness in the modeling framework. The long-term educational goal is to broaden the participation of K-12 and college students (in particular women and underrepresented minorities in STEM) in the fields of Operations Research and Applied Mathematics. In pursuit of this goal, the educational objective of this CAREER project is to inspire and engage young minds, formal and informal educators, and undergraduate and graduate students in understanding the role of optimization in tomorrow’s practice. This includes the following activities: (i) provide four-week professional development workshops for secondary teachers; (ii) develop an after school STEM program for Stillwater High School students; (iii) involve underrepresented undergraduate students in the PI’s research in collaboration with The Oklahoma Louis Stokes Alliance for Minority Participation; and (iv) develop an undergraduate and an advanced doctoral course.This project is jointly funded by the Energy, Power, Control, and Networks Program (EPCN), the Established Program to Stimulate Competitive Research (EPSCoR), and the Operations Engineering Program (OE).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.