Geometry of Information Structures, Strategic Measures and Associated Control Topologies


In many areas of engineering and applied mathematics (including stochastic control, networked control, information theory, game theory) decentralization of information is a key aspect determining how to approach a problem. We define information structures, place various topologies on them, and study closedness, compactness and convexity properties on the strategic measures induced by information structures and decentralized control/decision policies under varying degree of relaxations with regard to access to private or common randomness. Ultimately, we present existence and tight approximation results for optimal decision/control policies. We discuss various lower bounding techniques, through relaxations and convex programs ranging from classically realizable and classically non-realizable (such as quantum and non-signaling) relaxations. For each of these, we establish closedness and convexity properties and also a hierarchy of correlation structures.

As a second main theme, we review and introduce various topologies on decision/control strategies defined independent of information structures, but for which information structures determine whether the topologies entail utility in arriving at existence, compactness, convexification or approximation results.

These approaches, which we term as the strategic measures approach and the control topology approach, lead to complementary results on existence, approximations and upper and lower bounds in optimal decentralized stochastic control. Connections with some classical results on control theory will be revisited and examples will be discussed.


S. Yuksel received his B.Sc. degree in Electrical and Electronics Engineering from Bilkent University (2001), and M.S. and Ph.D. degrees in Electrical and Computer Engineering from the University of Illinois at Urbana-Champaign in 2003 and 2006. He was a post-doctoral researcher at Yale University for a year before joining Queen’s University as an assistant professor in the Department of Mathematics and Statistics, where he is now a professor. His research interests are on stochastic control, networked and decentralized control, information theory and probability. Prof. Yuksel has has co-authored two books on networked control and stochastic control and has been awarded the 2013 CAIMS/PIMS Early Career Award in Applied Mathematics and NSERC Discovery Accelerator Supplement Award. He has co-organized several workshops on control theory and information theory, has been an Associate Editor for the IEEE Transactions on Automatic Control, Automatica, and Systems and Control Letters, and has served on the editorial boards of several conferences.