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Given a single trajectory of a dynamical system, we analyze the performance of the nonparametric least squares estimator (LSE).
On the statistical treatment of linear stochastic difference equations
Henry B Mann and Abraham Wald · 1943
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ϵ \epsilon -entropy and ϵ \epsilon -capacity of sets in functional spaces
Andrei N Kolmogorov and Vladimir M Tikhomirov · 1961
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Probability inequalities for sums of bounded random variables
Wassily Hoeffding · 1963
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Asymptotic evaluation of certain markov process expectations for large time, i
Monroe D Donsker and SR Srinivasa Varadhan · 1975
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Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems
Tze Leung Lai and Ching Zong Wei · 1982
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Asymptotic statistics , volume 3
Aad W Van der Vaart · 2000
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David Angeli · 2002
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A learning theory approach to system identification and stochastic adaptive control
Mathukumalli Vidyasagar and Rajeeva L Karandikar · 2006
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Introduction to Nonparametric Estimation
Alexandre B Tsybakov · 2009
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The generalization ability of online algorithms for dependent data
Alekh Agarwal and John C Duchi · 2012
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Asymptotic methods in statistical decision theory
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Online non-parametric regression
Alexander Rakhlin and Karthik Sridharan · 2014
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Learning with square loss: Localization through offset rademacher complexity
Tengyuan Liang, Alexander Rakhlin, and Karthik Sridharan · 2015
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Concentration inequalities for markov chains by marton couplings and spectral methods
Daniel Paulin · 2015
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Generalization bounds for non-stationary mixing processes
Vitaly Kuznetsov and Mehryar Mohri · 2017
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Information-theoretic analysis of generalization capability of learning algorithms
Aolin Xu and Maxim Raginsky · 2017
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Learning without mixing: Towards a sharp analysis of linear system identification
Max Simchowitz, Horia Mania, Stephen Tu, Michael I Jordan, and Benjamin Recht · 2018
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High-dimensional probability: An introduction with applications in data science , volume 47
Roman Vershynin · 2018
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Certainty equivalence is efficient for linear quadratic control
Finite-time identification of stable linear systems optimality of the least-squares estimator
Yassir Jedra and Alexandre Proutiere · 2020
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Information theoretic regret bounds for online nonlinear control
Sham Kakade, Akshay Krishnamurthy, Kendall Lowrey, Motoya Ohnishi, and Wen Sun · 2020
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Active learning for nonlinear system identification with guarantees
Horia Mania, Michael I Jordan, and Benjamin Recht · 2020
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Non-asymptotic and accurate learning of nonlinear dynamical systems
Yahya Sattar and Samet Oymak · 2020
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Naive exploration is optimal for online lqr
Max Simchowitz and Dylan Foster · 2020
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Horia Mania, Stephen Tu, and Benjamin Recht · 2019
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Non-asymptotic identification of lti systems from a single trajectory
Samet Oymak and Necmiye Ozay · 2019
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How much does your data exploration overfit? controlling bias via information usage
Daniel Russo and James Zou · 2019
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Near optimal finite time identification of arbitrary linear dynamical systems
Tuhin Sarkar and Alexander Rakhlin · 2019
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Finite sample analysis of stochastic system identification
Anastasios Tsiamis and George J Pappas · 2019
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High-dimensional statistics: A non-asymptotic viewpoint , volume 48
Martin J Wainwright · 2019
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Tightening mutual information-based bounds on generalization error
Yuheng Bu, Shaofeng Zou, and Venugopal V Veeravalli · 2020
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Reasoning about generalization via conditional mutual information
Thomas Steinke and Lydia Zakynthinou · 2020
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Regret bounds for adaptive nonlinear control
Nicholas M Boffi, Stephen Tu, and Jean-Jacques E Slotine · 2021
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Tighter expected generalization error bounds via wasserstein distance
Borja Rodríguez Gálvez, Germán Bassi, Ragnar Thobaben, and Mikael Skoglund · 2021
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Pac-bayes, mac-bayes and conditional mutual information: Fast rate bounds that handle general vc classes
Peter Grünwald, Thomas Steinke, and Lydia Zakynthinou · 2021
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Near-optimal offline and streaming algorithms for learning non-linear dynamical systems
Prateek Jain, Suhas S Kowshik, Dheeraj Nagaraj, and Praneeth Netrapalli · 2021
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Model learning predictive control in nonlinear dynamical systems
Sahin Lale, Kamyar Azizzadenesheli, Babak Hassibi, and Anima Anandkumar · 2021
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Information-theoretic generalization bounds for stochastic gradient descent
Gergely Neu, Gintare Karolina Dziugaite, Mahdi Haghifam, and Daniel M. Roy · 2021
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On the sample complexity of stability constrained imitation learning
Stephen Tu, Alexander Robey, Tingnan Zhang, and Nikolai Matni · 2021
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Regret lower bounds for learning linear quadratic gaussian systems
Ingvar Ziemann and Henrik Sandberg · 2022
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