Mean Field Teams

Team optimal control of decentralized systems has been an important research topic since the mid 1960s. Many of the initial research results were negative and showed that even simple dynamical systems with two agents can be difficult to design. Since then, various solution methodologies for the optimal control of decentralized systems have been proposed and there has been considerable progress in understanding the nature of system dynamics and the information structure under which these methodologies work.

In spite of this progress, there is a big gap between the theory and applications of optimal decentralized control. On the one hand, the envisioned applications"”which include networked control systems, swarm robotics, and modern power systems"”often consist of multiple interconnected dynamical systems and controllers. On the other hand, explicit optimal solutions are available for systems with only a few (often two or three) controllers. We present a model that attempts to reduce this gap between theory and applications.

In particular, we consider a model in which the dynamics of an agent are influenced by the state of the others only through the mean-field of the population. We investigate team optimal control of such systems. By exploiting the exchageability of the agents, we identify an information state and use it to obtain a dynamic programming decomposition of the system. Our solution provides team optimal solution for systems with arbitrary number of agents. The complexity of the solution increases exponentially with the number of agents that allows us solve systems with moderate (100s to 1000s) number of agents.

Joint work with Jalal Arabneydi (Concordia University)
Aditya Mahajan is Associate Professor of Electrical and Computer Engineering at McGill University, Montreal, QC, Canada. He is a member of the McGill Center of Intelligent Machines (CIM) and Groupe d'tudes et de recherche en analyse des décisions (GERAD). He received the B.Tech degree in Electrical Engineering from the Indian Institute of Technology, Kanpur, India in 2003 and the MS and PhD degrees in Electrical Engineering and Computer Science from the University of Michigan, Ann Arbor, USA in 2006 and 2008. From 2008 to 2010, he was postdoctoral researcher in the department of Electrical Engineering at Yale University, New Haven, CT, USA. From 2016 to 2017, he was a visiting scholar at the University of California, Berkeley.

He is a senior member of the IEEE and member of SIAM and Professional Engineers Ontario. He currently serves as Associate Editor of Springer Mathematics of Control, Signal, and Systems and of the IEEE Control Systems Society Conference Editorial Board. He has co-organized the Workshop on Sequential and Adaptive Information Theory (2013), Banff workshop on Optimal Cooperation, Communication, and Learning in Decentralized Systems (2014), and Workshop on Information, Decisions, and Networks (2016). He is the recipient of the 2016 NSERC Discovery Accelerator Award, 2015 George Axelby Outstanding Paper Award, 2014 CDC Best Student Paper Award (as supervisor), and the 2016 NecSys Best Student Paper Award (as supervisor).

His principal research interests include decentralized stochastic control, team theory, multi-armed bandits, real-time communication, information theory, and discrete event systems.