1. Learning Linear Dynamics from Bilinear Observations
- Author
-
Sattar, Yahya, Jedra, Yassir, and Dean, Sarah
- Subjects
Computer Science - Machine Learning ,Electrical Engineering and Systems Science - Systems and Control ,Mathematics - Optimization and Control ,Statistics - Machine Learning - Abstract
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
- Published
- 2024