CAREER: Distributed Multi-Agent Control and Optimization: Where Game Theory Meets Network Optimization

本项目的研究目标是为分布式多智能体控制与优化问题的分析建立新的理论基础。重点将放在互联网和电力市场等大规模网络系统上，这些系统是由各种独立系统和具有不同性能标准的用户相互连接而产生的。分析这种网络中的最优资源分配需要一种基于博弈论（多智能体决策问题的研究）的新的控制范式。本研究的主要目标是研究不同类型网络中资源分配问题的博弈论模型，该模型考虑了具有竞争目标的代理之间的战略交互。该研究将解决分布式平衡模型的最坏情况性能损失的量化问题，并且对于损失较高的应用，将考虑集中控制方案以恢复接近最优的性能。另一个主要目标是开发新的数学工具来分析在这些设置中出现的非凸优化和平衡问题。议程包括使用和扩展微分拓扑的强大工具来研究非凸对策和优化问题中的平衡/平稳点，并设计有效的计算方法来计算平衡。这些研究活动伴随着一项教育计划，旨在影响麻省理工学院和更广泛的科学界。特别是，该计划包括为运筹学和工程专业的学生开设博弈论与应用的新课程（课程材料发表在麻省理工学院的开放课件计划中），重组现有的优化课程以教授前沿研究，并为这些领域的研究生和本科生提供建议。这项研究的结果有望通过对优化和博弈理论以及大规模网络分析方面的现有知识做出贡献而产生更广泛的影响。该研究将为分析网络系统的分布式控制提供一种新的方法。该项目的成功完成将产生健壮的网络控制协议和架构，并为通信网络提供性能保证和服务质量增强。这个框架不仅适用于工程系统，而且对建模和理解社会网络和敌对环境中的交互也很有用。整个研究计划还将在不同学科（运筹学、电气工程、理论计算机科学和经济学）之间创造协同效应，这些学科被调查的范围所跨越。

The research objective of this Faculty Early Career Development (CAREER)proposes to establish new theoretical foundations for the analysis of distributed multi-agent control and optimization problems. The focus will be on large-scale networked-systems, such as Internet and electricity markets, which have emerged from the interconnection of various independent systems and users with different performance criteria. The analysis of optimal resource allocation in such networks necessitates a new control paradigm, based on game theory (study of multi-agent decision problems). A primary objective of this research is to study game-theoretic models for resource allocation problems in different types of networks that take into account strategic interactions between agents with competing objectives. The research will address the question of quantification of the worst-case performance loss of the distributed equilibrium models, and for applications where the loss is high, will consider centralized control schemes to recover near-optimal performance. Another primary objective is to develop new mathematical tools for the analysis of non-convex optimization and equilibrium problems that arise in these settings. The agenda includes using and extending powerful tools from differential topology to study equilibrium/stationary points in non-convex games and optimization problems, and devising efficient computational methods to compute the equilibrium. The research activities are accompanied by an education plan, targeted to impact MIT and the broader scientific community. In particular, the plan includes teaching of a new course on game theory and applications for operations research and engineering students (with the course materials published in Open Courseware program of MIT), restructuring existing optimization courses to teach frontier research, and advising graduate and undergraduate students in these areas. The results of this research are expected to have a broader impact by contributing to existing knowledge both in the theory of optimization and games, and in the analysis of large-scale networks. The research will introduce a new approach for the analysis of distributed control of networked-systems. Successful completion of this project will result in robust network control protocols and architectures with performance guarantees and service quality enhancements for communication networks. This framework is not only applicable for engineered systems, but also is useful for modeling and understanding interactions in social networks and adversarial environments. The overall research program will also create synergies between the different disciplines (operations research, electrical engineering, theoretical computer science, and economics) that are spanned by the scope of the investigation.