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This tutorial survey provides an overview of recent non-asymptotic advances in statistical learning theory as relevant to control and system identification.
On the statistical treatment of linear stochastic difference equations
Henry B Mann and Abraham Wald · 1943
Earlier work this paper cites.
Dynamic programming under uncertainty with a quadratic criterion function
Herbert A Simon · 1956
Earlier work this paper cites.
Gradient methods for minimizing functionals
Boris Teodorovich Polyak · 1963
Earlier work this paper cites.
Perturbation bounds in connection with singular value decomposition
Per-Åke Wedin · 1972
Earlier work this paper cites.
On self tuning regulators
Karl Johan Åström and Björn Wittenmark · 1973
Earlier work this paper cites.
Modern wiener-hopf design of optimal controllers–part ii: The multivariable case
Dante Youla, Hamid Jabr, and Jr Bongiorno · 1976
Earlier work this paper cites.
Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses
George Zames · 1981
Earlier work this paper cites.
Asymptotic Properties of General Autoregressive Models and Strong Consistency of Least-Squares Estimates of Their Parameters
TL Lai and CZ Wei · 1983
Earlier work this paper cites.
Persistency of excitation, sufficient richness and parameter convergence in discrete time adaptive control
Er-Wei Bai and Sosale Shankara Sastry · 1985
Earlier work this paper cites.
Will the self-tuning approach work for general cost criteria?
Woei Lin, PR Kumar, and TI Seidman · 1985
Earlier work this paper cites.
Asymptotically efficient adaptive control in stochastic regression models
Tze Leung Lai · 1986
Earlier work this paper cites.
Optimal experiment designs with respect to the intended model application
Michel Gevers and Lennart Ljung · 1986
Earlier work this paper cites.
On the necessity of identifying the true parameter in adaptive lq control
Jan Willem Polderman · 1986
Earlier work this paper cites.
Asymptotic properties of the least-squares method for estimating transfer functions and disturbance spectra
Lennart Ljung and Bo Wahlberg · 1992
Earlier work this paper cites.
The sample complexity of worst-case identification of FIR linear systems
Munther A Dahleh, Theodore V Theodosopoulos, and John N Tsitsiklis · 1993
Earlier work this paper cites.
Perturbation analysis of the discrete riccati equation
Michail M Konstantinov, P Hr Petkov, and Nikolai D Christov · 1993
Earlier work this paper cites.
On the time complexity of worst-case system identification
Kameshwar Poolla and Ashok Tikku · 1994
Earlier work this paper cites.
Consistency and relative efficiency of subspace methods
Manfred Deistler, K Peternell, and Wolfgang Scherrer · 1995
Earlier work this paper cites.
Performance analysis of general tracking algorithms
Lei Guo and Lennart Ljung · 1995
Earlier work this paper cites.
Applications of the van trees inequality: a bayesian cramér-rao bound
Richard D Gill and Boris Y Levit · 1995
Earlier work this paper cites.
Nonparametric estimation of transfer functions: rates of convergence and adaptation
Alexander Goldenshluger · 1998
Earlier work this paper cites.
System Identification: Theory for the User
Lennart Ljung · 1999
Earlier work this paper cites.
Consistency and asymptotic normality of some subspace algorithms for systems without observed inputs
Dietmar Bauer, Manfred Deistler, and Wolfgang Scherrer · 1999
Earlier work this paper cites.
Finite sample properties of linear model identification
Erik Weyer, Robert C Williamson, and Iven MY Mareels · 1999
Earlier work this paper cites.
On the impact of weighting matrices in subspace algorithms
Dietmar Bauer, Manfred Deistler, and Wolfgang Scherrer · 2000
Earlier work this paper cites.
Finite sample properties of system identification methods
Marco C Campi and Erik Weyer · 2002
Earlier work this paper cites.
Strong converse for identification via quantum channels
Rudolf Ahlswede and Andreas Winter · 2002
Earlier work this paper cites.
Estimating cointegrated systems using subspace algorithms
Dietmar Bauer and Martin Wagner · 2002
Earlier work this paper cites.
Discrete-time stochastic systems: estimation and control
Torsten Söderström · 2002
Earlier work this paper cites.
The asymptotic variance of subspace estimates
Alessandro Chiuso and Giorgio Picci · 2004
Earlier work this paper cites.
Optimal Filtering
B.D.O. Anderson and J.B. Moore · 2005
Earlier work this paper cites.
Identification for Control: From the Early Achievements to the Revival of Experiment Design
Michel Gevers · 2005
Earlier work this paper cites.
An overview of subspace identification
S Joe Qin · 2006
Earlier work this paper cites.
Filtering and system identification: a least squares approach
Michel Verhaegen and Vincent Verdult · 2007
Earlier work this paper cites.
A learning theory approach to system identification and stochastic adaptive control
M Vidyasagar and Rajeeva L Karandikar · 2008
Earlier work this paper cites.
Simultaneous analysis of lasso and dantzig selector
Peter J Bickel, Ya’acov Ritov, and Alexandre B Tsybakov · 2009
Earlier work this paper cites.
A unified framework for high-dimensional analysis of m m -estimators with decomposable regularizers
Sahand Negahban, Bin Yu, Martin J Wainwright, and Pradeep Ravikumar · 2009
Earlier work this paper cites.
Regret Bounds for the Adaptive Control of Linear Quadratic Systems
Yasin Abbasi-Yadkori and Csaba Szepesvári · 2011
Earlier work this paper cites.
Improved algorithms for linear stochastic bandits
Yasin Abbasi-Yadkori, Dávid Pál, and Csaba Szepesvári · 2011
Earlier work this paper cites.
The statistical theory of linear systems
Edward James Hannan and Manfred Deistler · 2012
Earlier work this paper cites.
Subspace identification for linear systems: Theory–Implementation–Applications
Peter Van Overschee and Bart De Moor · 2012
Cited alongside, same era.
Concentration Inequalities: A Nonasymptotic Theory of Independence
Stéphane Boucheron, Gábor Lugosi, and Pascal Massart · 2013
Cited alongside, same era.
Learning without concentration
Shahar Mendelson · 2014
Cited alongside, same era.
Continuous control with deep reinforcement learning
Timothy P Lillicrap, Jonathan J Hunt, Alexander Pritzel, Nicolas Heess, Tom Erez, Yuval Tassa, David Silver, and Daan Wierstra · 2015
Cited alongside, same era.
A comprehensive survey on safe reinforcement learning
Javier Garcıa and Fernando Fernández · 2015
Cited alongside, same era.
Online learning for adversaries with memory: price of past mistakes
Naive Exploration is Optimal for Online LQR
Max Simchowitz and Dylan J Foster · 2020
Later among the works it cites.
Non-asymptotic Closed-Loop System Identification using Autoregressive Processes and Hankel Model Reduction
Bruce Lee and Andrew Lamperski · 2020
Later among the works it cites.
Non-asymptotic identification of linear dynamical systems using multiple trajectories
Yang Zheng and Na Li · 2020
Later among the works it cites.
Input Perturbations for Adaptive Control and Learning
Mohamad Kazem Shirani Faradonbeh, Ambuj Tewari, and George Michailidis · 2020
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Logarithmic Regret for Learning Linear Quadratic Regulators Efficiently
Asaf Cassel, Alon Cohen, and Tomer Koren · 2020
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Oren Anava, Elad Hazan, and Shie Mannor · 2015
Cited alongside, same era.
Mastering the game of go with deep neural networks and tree search
David Silver, Aja Huang, Chris J Maddison, Arthur Guez, Laurent Sifre, George Van Den Driessche, Julian Schrittwieser, Ioannis Antonoglou, Veda Panneershelvam, Marc Lanctot, et al · 2016
Cited alongside, same era.
The lower tail of random quadratic forms with applications to ordinary least squares
Roberto Imbuzeiro Oliveira · 2016
Cited alongside, same era.
Low-rank Solutions of Linear Matrix Equations via Procrustes Flow
Stephen Tu, Ross Boczar, Max Simchowitz, Mahdi Soltanolkotabi, and Ben Recht · 2016
Cited alongside, same era.
Linear convergence of gradient and proximal-gradient methods under the Polyak-Łojasiewicz condition
Hamed Karimi, Julie Nutini, and Mark Schmidt · 2016
Cited alongside, same era.
Non-asymptotic analysis of robust control from coarse-grained identification
Stephen Tu, Ross Boczar, Andrew Packard, and Benjamin Recht · 2017
Cited alongside, same era.
Control of unknown linear systems with Thompson sampling
Yi Ouyang, Mukul Gagrani, and Rahul Jain · 2017
Cited alongside, same era.
Improper learning for non-stochastic control
Max Simchowitz, Karan Singh, and Elad Hazan · 2020
Later among the works it cites.
Efficient optimistic exploration in linear-quadratic regulators via Lagrangian relaxation
Marc Abeille and Alessandro Lazaric · 2020
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Logarithmic regret bound in partially observable linear dynamical systems
Sahin Lale, Kamyar Azizzadenesheli, Babak Hassibi, and Anima Anandkumar · 2020
Later among the works it cites.
Online learning of the kalman filter with logarithmic regret
Anastasios Tsiamis and George Pappas · 2020
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No-regret prediction in marginally stable systems
Udaya Ghai, Holden Lee, Karan Singh, Cyril Zhang, and Yi Zhang · 2020
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Slip: Learning to predict in unknown dynamical systems with long-term memory
Paria Rashidinejad, Jiantao Jiao, and Stuart Russell · 2020
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Non-asymptotic and accurate learning of nonlinear dynamical systems
Yahya Sattar and Samet Oymak · 2020
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Learning nonlinear dynamical systems from a single trajectory
Dylan Foster, Tuhin Sarkar, and Alexander Rakhlin · 2020
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Least squares regression with markovian data: Fundamental limits and algorithms
Dheeraj Nagaraj, Xian Wu, Guy Bresler, Prateek Jain, and Praneeth Netrapalli · 2020
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Linear Systems can be Hard to Learn
Anastasios Tsiamis and George J. Pappas · 2021
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Finite impulse response models: A non-asymptotic analysis of the least squares estimator
Boualem Djehiche, Othmane Mazhar, and Cristian R Rojas · 2021
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Finite time LTI system identification
Tuhin Sarkar, Alexander Rakhlin, and Munther A Dahleh · 2021
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Revisiting Ho-Kalman based system identification: robustness and finite-sample analysis
Samet Oymak and Necmiye Ozay · 2021
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Learning partially observed linear dynamical systems from logarithmic number of samples
Salar Fattahi · 2021
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Adaptive control and regret minimization in linear quadratic gaussian (LQG) setting
Sahin Lale, Kamyar Azizzadenesheli, Babak Hassibi, and Anima Anandkumar · 2021
Later among the works it cites.
Learning optimal controllers by policy gradient: Global optimality via convex parameterization
Yue Sun and Maryam Fazel · 2021
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Task-optimal exploration in linear dynamical systems
Andrew J Wagenmaker, Max Simchowitz, and Kevin Jamieson · 2021
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Policy gradient methods for the noisy linear quadratic regulator over a finite horizon
Ben Hambly, Renyuan Xu, and Huining Yang · 2021
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Stabilizing dynamical systems via policy gradient methods
Juan Perdomo, Jack Umenberger, and Max Simchowitz · 2021
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Identification and adaptive control of markov jump systems: Sample complexity and regret bounds
Yahya Sattar, Zhe Du, Davoud Ataee Tarzanagh, Laura Balzano, Necmiye Ozay, and Samet Oymak · 2021
Later among the works it cites.
Near-optimal offline and streaming algorithms for learning non-linear dynamical systems
Suhas Kowshik, Dheeraj Nagaraj, Prateek Jain, and Praneeth Netrapalli · 2021
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Contraction theory for nonlinear stability analysis and learning-based control: A tutorial overview
Hiroyasu Tsukamoto, Soon-Jo Chung, and Jean-Jaques E Slotine · 2021
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A note on the smallest eigenvalue of the empirical covariance of causal gaussian processes
Ingvar Ziemann · 2022
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Exact minimax risk for linear least squares, and the lower tail of sample covariance matrices
Jaouad Mourtada · 2022
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Improved rates for prediction and identification of partially observed linear dynamical systems
Holden Lee · 2022
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System Identification via Nuclear Norm Regularization
Yue Sun, Samet Oymak, and Maryam Fazel · 2022
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Efficient learning of hidden state LTI state space models of unknown order
Boualem Djehiche and Othmane Mazhar · 2022
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Near-optimal design of safe output feedback controllers from noisy data
Luca Furieri, Baiwei Guo, Andrea Martin, and Giancarlo Ferrari-Trecate · 2022
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Towards a theoretical foundation of policy optimization for learning control policies
Bin Hu, Kaiqing Zhang, Na Li, Mehran Mesbahi, Maryam Fazel, and Tamer Başar · 2022
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Regret lower bounds for learning linear quadratic gaussian systems
Ingvar Ziemann and Henrik Sandberg · 2022
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Learning to control linear systems can be hard
Anastasios Tsiamis, Ingvar Ziemann, Manfred Morari, Nikolai Matni, and George J. Pappas · 2022
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Regret minimization for linear quadratic adaptive controllers using fisher feedback exploration
Kévin Colin, Mina Ferizbegovic, and Håkan Hjalmarsson · 2022
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Ingvar Ziemann and Stephen Tu · 2022
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Active learning for nonlinear system identification with guarantees
Horia Mania, Michael I Jordan, and Benjamin Recht · 2022
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Tasil: Taylor series imitation learning
Daniel Pfrommer, Thomas TCK Zhang, Stephen Tu, and Nikolai Matni · 2022
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