Title: Prof. Dominic Liao-McPherson

Abstract: Many iterative algorithms in optimization, games, and learning can be viewed as dynamical systems with inputs (measurements, historical data, user feedback), internal states (decision variables, state estimates, Lagrange multipliers), outputs (actuator commands), and uncertainties (noise, unknown parameters). The last few years have witnessed a growing interest in studying how learning and optimization behave when placed in closed loop with physical systems and conversely how systems theory can be leveraged to both analyze existing algorithms and synthesize new ones. This dynamical systems perspective on algorithms is crucial for tackling some of the challenges arising when analyzing and synthesizing the algorithms that underlie modern autonomous, AI-driven, and socio-technical systems. These include algorithms that: (i) operate online (e.g., algorithms with streaming data), (ii) include humans in the loop (e.g., recommender systems), (iii) are interconnected with physical systems (e.g., real-time MPC), or (iv) need to be robust to severe uncertainty (e.g., exogenous disturbances, intrinsic randomness). These applications are driving the development of new theoretical tools that synergistically build on control, optimization, and learning theory to build algorithms that are specialized for noisy, time-varying, and dynamic environments. In this talk, I discuss two scenarios where optimization algorithms are used directly as controllers for physical systems. First, I present Time-distributed Optimization (TDO), a unifying framework for studying the system theoretic consequences of computational limits in the context of Model Predictive Control (MPC). I show that it is possible to recover the stability and robustness properties of optimal MPC despite limited computational resources and illustrate how a system-theoretic view of algorithms can be exploited to certify the closed-loop system and illustrate the applicability of the these methods in the real-world examples. Second, I discuss Feedback Equilibrium Seeking (FES), a design framework for dynamic feedback controllers that track solution trajectories of time-varying generalized equations, such as local minimizers of nonlinear programs or competitive equilibria (e.g., Nash) of non-cooperative games. I present tracking error, stability, and robustness results for the sampled-data cased and provide illustrative examples.

Biography: Dominic Liao-McPherson received his BASc in Engineering Science from the University of Toronto in 2015 and a PhD in Aerospace Engineering and Scientific Computing from the University of Michigan (Ann Arbor) in 2020. He was a postdoc at the ETH Zurich Automatic Control Lab (ifA) between 2020 and 2022 before joining the University of British Columbia as an Assistant Professor of Mechanical Engineering in 2023. His research interests lie at the intersection of optimization, control, game-theory, and computing with applications in robotics, energy, and aerospace systems.