Generalization bounds for non-stationary mixing processes

Kuznetsov, Vitaly; Mohri, Mehryar

doi:10.1007/s10994-016-5588-2

Cited by 50 publications

(41 citation statements)

References 25 publications

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“…They also prove that their rate is minimax optimal. More recently, several authors [34,40,43] have studied generalization bounds for non i.i.d. data, extending the standard learning theory guarantees for independent data.…”

Section: Related Workmentioning

confidence: 99%

On the Sample Complexity of the Linear Quadratic Regulator

et al. 2019

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This paper addresses the optimal control problem known as the Linear Quadratic Regulator in the case when the dynamics are unknown. We propose a multi-stage procedure, called Coarse-ID control, that estimates a model from a few experimental trials, estimates the error in that model with respect to the truth, and then designs a controller using both the model and uncertainty estimate. Our technique uses contemporary tools from random matrix theory to bound the error in the estimation procedure. We also employ a recently developed approach to control synthesis called System Level Synthesis that enables robust control design by solving a quasiconvex optimization problem. We provide end-to-end bounds on the relative error in control cost that are optimal in the number of parameters and that highlight salient properties of the system to be controlled such as closed-loop sensitivity and optimal control magnitude. We show experimentally that the Coarse-ID approach enables efficient computation of a stabilizing controller in regimes where simple control schemes that do not take the model uncertainty into account fail to stabilize the true system.

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Section: Related Workmentioning

confidence: 99%

On the Sample Complexity of the Linear Quadratic Regulator

et al. 2019

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“…Note that PAC bounds for learning time series has been explored in the literature by Kuznetsov and Mohri (2017;2018). Their approach is based on covering numbers and Rademacher complexity instead of PAC-Bayes analysis, but in contrast to the current paper, Kuznetsov and Mohri's work allows for non-stationary time series.…”

Section: Related Workmentioning

confidence: 99%

Improved PAC-Bayesian Bounds for Linear Regression

Shalaeva

Esfahani

Germain

et al. 2020

AAAI

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In this paper, we improve the PAC-Bayesian error bound for linear regression derived in Germain et al. (2016). The improvements are two-fold. First, the proposed error bound is tighter, and converges to the generalization loss with a well-chosen temperature parameter. Second, the error bound also holds for training data that are not independently sampled. In particular, the error bound applies to certain time series generated by well-known classes of dynamical models, such as ARX models.

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“…We do not give an account here on the developments of these topics for dependent, nonstationary designs because they escape the specific purpose of the present paper. For an exposition in this direction, see [KM17] and the references therein.…”

Section: Background Results In the Literaturementioning

confidence: 99%