Online Learning of Parameterized Uncertain Dynamical Environments With Finite-Sample Guarantees

We present a novel online learning algorithm for a class of unknown and uncertain dynamical environments that are fully observable. First, we obtain a novel probabilistic characterization of systems whose mean behavior is known but which are subject to additive, unknown subGaussian disturbances. This characterization relies on recent concentration of measure results and is given in terms of ambiguity sets. Second, we extend the results to environments whose mean behavior is also unknown but described by a parameterized class of possible mean behaviors. Our algorithm adapts the ambiguity set dynamically by learning the parametric dependence online, and retaining similar probabilistic guarantees with respect to the additive, unknown disturbance. We illustrate the results on a differential-drive robot subject to environmental uncertainty.

[1]  Auke Jan Ijspeert,et al.  Learning to Move in Modular Robots using Central Pattern Generators and Online Optimization , 2008, Int. J. Robotics Res..

[2]  Sonia Martínez,et al.  Dynamic Evolution of Distributional Ambiguity Sets and Precision Tradeoffs in Data Assimilation , 2019, 2019 18th European Control Conference (ECC).

[3]  Jing Lei.  Convergence and concentration of empirical measures under Wasserstein distance in unbounded functional spaces , 2018, Bernoulli.

[4]  Samet Oymak,et al.  Non-asymptotic Identification of LTI Systems from a Single Trajectory , 2018, 2019 American Control Conference (ACC).

[5]  Carlo Novara,et al.  Unified Set Membership theory for identification, prediction and filtering of nonlinear systems , 2011, Autom..

[6]  V. Verdult,et al.  Filtering and System Identification: A Least Squares Approach , 2007 .

[7]  Jonathan Niles-Weed,et al.  Estimation of Wasserstein distances in the Spiked Transport Model , 2019, Bernoulli.

[8]  Sonia Martínez,et al.  Online Learning of Parameterized Uncertain Dynamical Environments with Finite-sample Guarantees , 2021, 2021 American Control Conference (ACC).

[9]  Alessandro Chiuso,et al.  System Identification: A Machine Learning Perspective , 2019, Annu. Rev. Control. Robotics Auton. Syst..

[10]  Giuseppe C. Calafiore,et al.  Nonlinear system identification in Sobolev spaces , 2019, Int. J. Control.

[11]  O. Papaspiliopoulos.  High-Dimensional Probability: An Introduction with Applications in Data Science , 2020 .

[12]  A. Guillin,et al.  On the rate of convergence in Wasserstein distance of the empirical measure , 2013, 1312.2128.

[13]  George J. Pappas,et al.  Finite Sample Analysis of Stochastic System Identification , 2019, 2019 IEEE 58th Conference on Decision and Control (CDC).

[14]  Dimitris Boskos,et al.  Data-Driven Ambiguity Sets With Probabilistic Guarantees for Dynamic Processes , 2019, IEEE Transactions on Automatic Control.

[15]  Alexander Rakhlin,et al.  Near optimal finite time identification of arbitrary linear dynamical systems , 2018, ICML.

[16]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[17]  Roman Vershynin,et al.  High-Dimensional Probability , 2018 .

[18]  Steven M. LaValle,et al.  Planning algorithms , 2006 .

[19]  Biao Huang,et al.  System Identification , 2000, Control Theory for Physicists.

[20]  Nikolai Matni,et al.  Learning Sparse Dynamical Systems from a Single Sample Trajectory , 2019, 2019 IEEE 58th Conference on Decision and Control (CDC).

[21]  Michael C. Yip,et al.  Motion Planning Networks: Bridging the Gap Between Learning-Based and Classical Motion Planners , 2019, IEEE Transactions on Robotics.