Learning Neural Networks under Input-Output Specifications

In this paper, we examine an important problem of learning neural networks that certifiably meet certain specifications on input-output behaviors. Our strategy is to find an inner approximation of the set of admissible policy parameters, which is convex in a transformed space. To this end, we addres...

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Bibliographic Details
Main Authors Abdeen, Zain ul, Yin, He, Kekatos, Vassilis, Jin, Ming
Format Journal Article
LanguageEnglish
Published 22.02.2022
Subjects
Computer Science - Learning
Computer Science - Systems and Control
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Summary:In this paper, we examine an important problem of learning neural networks that certifiably meet certain specifications on input-output behaviors. Our strategy is to find an inner approximation of the set of admissible policy parameters, which is convex in a transformed space. To this end, we address the key technical challenge of convexifying the verification condition for neural networks, which is derived by abstracting the nonlinear specifications and activation functions with quadratic constraints. In particular, we propose a reparametrization scheme of the original neural network based on loop transformation, which leads to a convex condition that can be enforced during learning. This theoretical construction is validated in an experiment that specifies reachable sets for different regions of inputs.
DOI:10.48550/arxiv.2202.11246