Recovering and Steering Belief States in Partially Observed Systems
Auto-regressive models, trained simply to predict future observations from past ones, have become a default tool for sequential data, from language to video to control-relevant time series. Their learned representations are increasingly repurposed for downstream planning, estimation, and control. Yet we lack rigorous understanding of what these representations capture, which matters if we want to use them in closed-loop, safety-critical systems.
This talk first addresses that gap in a canonical setting: partially observed linear dynamical systems, where the optimal recursive estimator is the Kalman filter. We study a two-layer linear auto-regressive model trained by empirical risk minimization on input-output data alone, with no knowledge of the dynamics, noise, or state. We show that this model probably learns a hidden representation matching the Kalman filter's state estimate, up to a similarity transformation.
In linear systems, inputs shift the belief state but have no effect on how informative observations are. However, in many applications, from robotics to personalized recommendation, control actions both impact the system state and our uncertainty about it. We conclude with a discussion of a class of systems which captures these observer effects, recent results on learning and control, and several open questions.
Biography
Sarah Dean is an assistant professor of computer science at Cornell University. She studies the interplay between optimization, machine learning, and dynamics in real-world systems. Her research focuses on understanding the fundamentals of data-driven methods for control and decision-making, inspired by applications ranging from robotics to recommendation systems. She completed her postdoctoral research at the University of Washington and earned her M.S. and Ph.D. in electrical engineering and computer science at the University of California, Berkeley. Dean received her B.S.E. in electrical engineering and mathematics from the University of Pennsylvania.
