Certification of iterative predictions in Bayesian neural networks

Matthew Wicker, Luca Laurenti, Andrea Patane, Nicola Paoletti, Alessandro Abate, Marta Kwiatkowska
Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, PMLR 161:1713-1723, 2021.

Abstract

We consider the problem of computing reach-avoid probabilities for iterative predictions made with Bayesian neural network (BNN) models. Specifically, we leverage bound propagation techniques and backward recursion to compute lower bounds for the probability that trajectories of the BNN model reach a given set of states while avoiding a set of unsafe states. We use the lower bounds in the context of control and reinforcement learning to provide safety certification for given control policies, as well as to synthesize control policies that improve the certification bounds. On a set of benchmarks, we demonstrate that our framework can be employed to certify policies over BNNs predictions for problems of more than $10$ dimensions, and to effectively synthesize policies that significantly increase the lower bound on the satisfaction probability.

Cite this Paper

BibTeX
@InProceedings{pmlr-v161-wicker21a, title = {Certification of iterative predictions in {B}ayesian neural networks}, author = {Wicker, Matthew and Laurenti, Luca and Patane, Andrea and Paoletti, Nicola and Abate, Alessandro and Kwiatkowska, Marta}, booktitle = {Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence}, pages = {1713--1723}, year = {2021}, editor = {de Campos, Cassio and Maathuis, Marloes H.}, volume = {161}, series = {Proceedings of Machine Learning Research}, month = {27--30 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v161/wicker21a/wicker21a.pdf}, url = {https://proceedings.mlr.press/v161/wicker21a.html}, abstract = {We consider the problem of computing reach-avoid probabilities for iterative predictions made with Bayesian neural network (BNN) models. Specifically, we leverage bound propagation techniques and backward recursion to compute lower bounds for the probability that trajectories of the BNN model reach a given set of states while avoiding a set of unsafe states. We use the lower bounds in the context of control and reinforcement learning to provide safety certification for given control policies, as well as to synthesize control policies that improve the certification bounds. On a set of benchmarks, we demonstrate that our framework can be employed to certify policies over BNNs predictions for problems of more than $10$ dimensions, and to effectively synthesize policies that significantly increase the lower bound on the satisfaction probability.} }
Endnote
%0 Conference Paper %T Certification of iterative predictions in Bayesian neural networks %A Matthew Wicker %A Luca Laurenti %A Andrea Patane %A Nicola Paoletti %A Alessandro Abate %A Marta Kwiatkowska %B Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2021 %E Cassio de Campos %E Marloes H. Maathuis %F pmlr-v161-wicker21a %I PMLR %P 1713--1723 %U https://proceedings.mlr.press/v161/wicker21a.html %V 161 %X We consider the problem of computing reach-avoid probabilities for iterative predictions made with Bayesian neural network (BNN) models. Specifically, we leverage bound propagation techniques and backward recursion to compute lower bounds for the probability that trajectories of the BNN model reach a given set of states while avoiding a set of unsafe states. We use the lower bounds in the context of control and reinforcement learning to provide safety certification for given control policies, as well as to synthesize control policies that improve the certification bounds. On a set of benchmarks, we demonstrate that our framework can be employed to certify policies over BNNs predictions for problems of more than $10$ dimensions, and to effectively synthesize policies that significantly increase the lower bound on the satisfaction probability.
APA
Wicker, M., Laurenti, L., Patane, A., Paoletti, N., Abate, A. & Kwiatkowska, M.. (2021). Certification of iterative predictions in Bayesian neural networks. Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 161:1713-1723 Available from https://proceedings.mlr.press/v161/wicker21a.html.

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