Prof. Tyler Summers, University of Texas at Dallas

Title: Belief Hierarchies and Dynamic Programming for LQG Games with Asymmetric Information

Abstract: Strategic interaction between agents with private and asymmetric information introduces fundamental difficulties that separate multi-agent games from their single-agent counterparts: the separation principle fails, optimal strategies are in general infinite-dimensional, and each agent must reason not just about the world but about the other agents’ beliefs, leading to an infinite regress of higher-order beliefs. This talk examines these challenges through the lens of linear-quadratic Gaussian (LQG) games, where the structure is rich enough to expose the difficulties clearly while remaining tractable enough to make progress.

We study the belief hierarchy that arises naturally from best-response dynamics. By iterating best responses, each player must track an internal state of growing dimension at every round: estimates of the state, of the opponent’s estimate, of the opponent’s estimate of the estimate, and so on. A key empirical finding, supported by Gramian and Hankel singular value analysis, is that this hierarchy exhibits rapid, often geometric, decay: the gain from reasoning one level deeper diminishes quickly, and in practice convergence occurs in a handful of iterations. This observation motivates fixing the internal state dimension a priori, leading to a class of approximate perfect Bayesian equilibria (APBE) computable by a forward-backward dynamic programming algorithm. The forward pass propagates coupled belief covariances, replacing the standard Kalman filter which breaks down due to inseparability of estimation and control, and the backward pass is a Riccati-type recursion over an augmented state carrying estimation errors alongside the physical state. Both finite-horizon and infinite-horizon variants are presented, along with numerical experiments on pursuit-evasion and target-attacker-defender scenarios. We close with a brief discussion of ongoing work on policy optimization via gradient descent-ascent methods.

Brief bio: Tyler Summers is an associate professor at the University of Texas at Dallas. Prior to joining UT Dallas, he was an ETH Postdoctoral Fellow at the Automatic Control Laboratory at ETH Zurich from 2011 to 2015. He received a PhD degree in Aerospace Engineering at the University of Texas at Austin in 2010. He was a Fulbright Postgraduate Scholar at the Australian National University in Canberra, Australia in 2007-2008. He received the National Science Foundation CAREER Award in 2021 and a Young Investigator Program award from the US Army Research Office in 2017. His research interests are in feedback control, optimization, and learning in complex dynamical networks, with applications in robotics and power networks.