Learning Linear Dynamics from Bilinear Observations
<|reference_start|>Learning Linear Dynamics from Bilinear Observations: 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.<|reference_end|>
@article{sattar2024learning,
    title={Learning Linear Dynamics from Bilinear Observations},
    author={Yahya Sattar, Yassir Jedra, Sarah Dean},
    journal={arXiv preprint arXiv:2409.16499},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.16499},
    primaryClass={cs.LG cs.SY eess.SY math.OC stat.ML}
}