Learning Linear Dynamics from Bilinear Observations

Autor:	Sattar, Yahya, Jedra, Yassir, Dean, Sarah
Rok vydání:	2024
Předmět:	Computer Science - Machine Learning Electrical Engineering and Systems Science - Systems and Control Mathematics - Optimization and Control Statistics - Machine Learning
Druh dokumentu:	Working Paper
Popis:	We consider the problem of learning a realization of a partially observed dynamical system with linear state transitions and bilinear observations. Under very mild assumptions on the process and measurement noises, we provide a finite time analysis for learning the unknown dynamics matrices (up to a similarity transform). Our analysis involves a regression problem with heavy-tailed and dependent data. Moreover, each row of our design matrix contains a Kronecker product of current input with a history of inputs, making it difficult to guarantee persistence of excitation. We overcome these challenges, first providing a data-dependent high probability error bound for arbitrary but fixed inputs. Then, we derive a data-independent error bound for inputs chosen according to a simple random design. Our main results provide an upper bound on the statistical error rates and sample complexity of learning the unknown dynamics matrices from a single finite trajectory of bilinear observations. Comment: 35 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.16499 Zobrazit plný text záznamu View this record from Arxiv