Abstract
Machine learning promises high-performance control, but is that always possible? Can the learned controller be inherently fragile? Even for linear systems, we still lack a clear understanding of the complexity of learning-based control.
In this talk, I present a framework for quantifying the statistical complexity of learning-based control, that is, the data requirements for achieving satisfactory closed-loop performance. Focusing on the Linear Quadratic Gaussian (LQG) setting, we will demonstrate that partial observability—long known to induce fragility in robust control—also fundamentally limits how efficiently controllers can be learned from data.
We study an offline learning setting, where data is collected from trajectories generated by an exploration policy. Our main result is a minimax lower bound that applies to any algorithm mapping data to a stabilizing linear controller. The bound reveals that the difficulty of learning is governed by two key quantities: i) the Hessian of the certainty-equivalent LQG cost with respect to the unknown model parameters and ii) the inverse Fisher Information induced by the exploration policy. Technically, the analysis leverages a quadratic characterization of the LQG suboptimality gap in the Youla parameter and the van Trees inequality.
We instantiate the bound on several examples, including a variant of the classical LQG fragility counterexample by John Doyle and a non-minimum-phase system example, demonstrating when fragile robust control problems translate into high sample complexity for learning-based control.
Biographical Information
Anastasios Tsiamis received the Diploma degree in electrical and computer engineering from the National Technical University of Athens, Greece, in 2014. He obtained his Ph.D. at the Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, USA in 2022. Currently, he is a senior scientist at the Automatic Control Laboratory, ETH Zurich, Switzerland. His research interests include statistical and online learning in the setting of control systems, as well as robust and risk-aware control. Anastasios Tsiamis was a finalist for the IFAC Young Author Prize in IFAC 2017 World Congress and a finalist for the Best Student Paper Award in ACC 2019. He is a coauthor to the paper that has won the Best Student Paper Award in CDC 2022.