Linear Systems can be Hard to Learn

R. Eising, “Between controllable and uncontrollable,” Systems & Control Letters , vol. 4, no. 5, pp. 263–264, 1984

1984

Earlier work this paper cites.

E.-W. Bai and S. S. Sastry, “Persistency of excitation, sufficient richness and parameter convergence in discrete time adaptive control,” Systems & control letters , vol. 6, no. 3, pp. 153–163, 1985

1985

Earlier work this paper cites.

M. Deistler, K. Peternell, and W. Scherrer, “Consistency and relative efficiency of subspace methods,” Automatica , vol. 31, no. 12, pp. 1865–1875, 1995

1995

Earlier work this paper cites.

L. Ljung, System Identification: Theory for the User . Prentice Hall, 1999

1999

Earlier work this paper cites.

D. Bauer, M. Deistler, and W. Scherrer, “Consistency and asymptotic normality of some subspace algorithms for systems without observed inputs,” Automatica , vol. 35, no. 7, pp. 1243–1254, 1999

1999

Earlier work this paper cites.

D. Kulkarni, D. Schmidt, and S.-K. Tsui, “Eigenvalues of tridiagonal pseudo-Toeplitz matrices,” Linear Algebra and its Applications , vol. 297, no. 1, pp. 63–80, 1999

1999

Earlier work this paper cites.

M. C. Campi and E. Weyer, “Finite sample properties of system identification methods,” IEEE Transactions on Automatic Control , vol. 47, no. 8, pp. 1329–1334, 2002

2002

Earlier work this paper cites.

P. M. V. Dooren, “Numerical linear algebra for signals systems and control,” Draft notes prepared for the Graduate School in Systems and Control , 2003

2003

Earlier work this paper cites.

A. Chiuso and G. Picci, “The asymptotic variance of subspace estimates,” Journal of Econometrics , vol. 118, no. 1-2, pp. 257–291, 2004

2004

Earlier work this paper cites.

R. A. Horn and C. R. Johnson, Matrix analysis , 2nd ed. Cambridge University Press, 2012

2012

Earlier work this paper cites.

S. Shalev-Shwartz and S. Ben-David, Understanding machine learning: From theory to algorithms . Cambridge university press, 2014

2014

Earlier work this paper cites.

S. Dean, H. Mania, N. Matni, B. Recht, and S. Tu, “On the sample complexity of the linear quadratic regulator,” arXiv preprint arXiv:1710.01688 , 2017

Original

2017

Earlier work this paper cites.

N. Jiang, A. Krishnamurthy, A. Agarwal, J. Langford, and R. E. Schapire, “Contextual decision processes with low Bellman rank are PAC-learnable,” in International Conference on Machine Learning . PMLR, 2017, pp. 1704–1713

2017

Cited alongside, same era.

C. Dann, T. Lattimore, and E. Brunskill, “Unifying PAC and regret: Uniform PAC bounds for episodic reinforcement learning,” arXiv preprint arXiv:1703.07710 , 2017

Original

2017

Cited alongside, same era.

R. Vershynin, High-dimensional probability: An introduction with applications in data science . Cambridge University Press, 2018, vol. 47

2018

Cited alongside, same era.

M. Simchowitz, H. Mania, S. Tu, M. I. Jordan, and B. Recht, “Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification,” arXiv preprint arXiv:1802.08334 , 2018

Original

2018

Cited alongside, same era.

A. Tsiamis and G. J. Pappas, “Finite Sample Analysis of Stochastic System Identification,” in IEEE 58th Conference on Decision and Control (CDC) , 2019

2019

Later among the works it cites.

B. Lee and A. Lamperski, “Non-asymptotic Closed-Loop System Identification using Autoregressive Processes and Hankel Model Reduction,” arXiv preprint arXiv:1909.02192 , 2019

Original

2019

Later among the works it cites.

M. Kozdoba, J. Marecek, T. Tchrakian, and S. Mannor, “On-line learning of linear dynamical systems: Exponential forgetting in Kalman filters,” in Proceedings of the AAAI Conference on Artificial Intelligence , vol. 33, 2019, pp. 4098–4105

2019

Later among the works it cites.

N. Matni and S. Tu, “A tutorial on concentration bounds for system identification,” in 2019 IEEE 58th Conference on Decision and Control (CDC) . IEEE, 2019, pp. 3741–3749

2019

Later among the works it cites.