ModelGuard: Runtime Validation of Lipschitz-continuous Models

This paper presents ModelGuard, a sampling-based approach to runtime model validation for Lipschitz-continuous models. Although techniques exist for the validation of many classes of models, the majority of these methods cannot be applied to the whole of Lipschitzcontinuous models, which includes neural network models. Additionally, existing techniques generally consider only white-box models. By taking a sampling-based approach, we can address black-box models, represented only by an input-output relationship and a Lipschitz constant. We show that by randomly sampling from a parameter space and evaluating the model, it is possible to guarantee the correctness of traces labeled consistent and provide a confidence on the correctness of traces labeled inconsistent. We evaluate the applicability and scalability of ModelGuard in three case studies, including a physical platform.

[1]  Insup Lee,et al.  Case study: verifying the safety of an autonomous racing car with a neural network controller , 2019, HSCC.

[2]  Constantino M. Lagoa,et al.  Convex Certificates for Model (In)validation of Switched Affine Systems With Unknown Switches , 2014, IEEE Transactions on Automatic Control.

[3]  Stephen Prajna Barrier certificates for nonlinear model validation , 2006, Autom..

[4]  Bernhard Pfahringer,et al.  Regularisation of neural networks by enforcing Lipschitz continuity , 2018, Machine Learning.

[5]  Tong Zhou,et al.  A probabilistic approach to model set validation , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[6]  Andrew W. Moore,et al.  Efficient memory-based learning for robot control , 1990 .

[7]  Mohammad Khajenejad,et al.  Data-Driven Model Invalidation for Unknown Lipschitz Continuous Systems via Abstraction , 2020, 2020 American Control Conference (ACC).

[8]  Xin Chen,et al.  Flow*: An Analyzer for Non-linear Hybrid Systems , 2013, CAV.

[9]  Philipp Rumschinski,et al.  A set-based framework for coherent model invalidation and parameter estimation of discrete time nonlinear systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[10]  Roy S. Smith,et al.  Model validation for nonlinear feedback systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[11]  Thomas Rauschenbach,et al.  UUV Simulator: A Gazebo-based package for underwater intervention and multi-robot simulation , 2016, OCEANS 2016 MTS/IEEE Monterey.

[12]  Alberto L. Sangiovanni-Vincentelli,et al.  Scenic: a language for scenario specification and scene generation , 2018, PLDI.

[13]  Insup Lee,et al.  Verisig: verifying safety properties of hybrid systems with neural network controllers , 2018, HSCC.

[14]  Manfred Morari,et al.  Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks , 2019, NeurIPS.