Learning for Optimization & Control IV – Invited Special Session

A5L-F: Learning for Optimization & Control IV - Invited Special Session

Session Type: Lecture
Session Code: A5L-F
Location: Room 6
Date & Time: Wednesday March 22, 2023 (15:20-16:20)
Chair: Mahyar Fazlyab, Enrique Mallada
Track: 12
Paper IDPaper NameAuthorsAbstract
3107Towards Optimal Sample Complexity for Learning Partially Observed Linear Dynamical SystemsHolden LeeIdentification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory. In this talk, I\'ll discuss the following questions: what are the optimal non-asymptotic rates at which we can learn such systems using efficient algorithms? Are they achieved by classical subspace identification algorithms, or can we design more sample-efficient algorithms informed by statistical learning theory? In particular, a big challenge is to obtain rates depending on the inherent dimensionality (order) d of the system, rather than other quantities such as the memory length of the system. We make progress towards this question by giving a new algorithm, based on a multi-scale low-rank approximation of Hankel matrices, which learns the system in H_2 error with near-optimal rates under observation noise. Based on https://arxiv.org/abs/2011.10006.
3137Federated Learning for System Identification and ControlHan Wang, Leonardo Toso, James AndersonWe study the problem of learning a linear system model from the observations of M clients. The catch: Each client is observing data from a different dynamical system. This work addresses the question of how multiple clients collaboratively learn dynamical models in the presence of heterogeneity. We pose this problem as a federated learning problem and characterize the tension between achievable performance and system heterogeneity. Furthermore, our federated sample complexity result provides a constant factor improvement over the single agent setting. We describe a meta federated learning algorithm, FedSysID, that leverages existing federated algorithms at the client level. Finally, joint and federated learning approaches to LQR synthesis via policy gradient methods will be described.
3169On the Sample Complexity of Stabilizing LTI Systems on a Single TrajectoryYang Hu{3}, Adam Wierman{1}, Guannan Qu{2}Stabilizing an unknown dynamical system is one of the central problems in control theory. In this paper, we study the sample complexity of the learn-to-stabilize problem in Linear Time-Invariant (LTI) systems on a single trajectory. Current state-of-the-art approaches require a sample complexity linear in $n$, the state dimension, which incurs a state norm that blows up exponentially in $n$. We propose a novel algorithm based on spectral decomposition that only needs to learn a small part of the dynamical matrix acting on its unstable subspace. We show that, under proper assumptions, our algorithm stabilizes an LTI system on a single trajectory with $\\tilde{O}(k)$ samples, where $k$ is the instability index of the system. This represents the first sub-linear sample complexity result for the stabilization of LTI systems under the regime when $k=o(n)$