@inproceedings{2022_2C_learning,
  title={Learning Neural Networks under Input-Output Specifications},
  author={Zain ul Abdeen and He Yin and Vassilis Kekatos and Ming Jin},
  booktitle={American Control Conference},
  pages={},
  year={2022},
  url_pdf={LearnNNSpecs.pdf},
  keywords = {Optimization, Machine Learning},
  abstract={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 computationally enforced during learning. The theoretical construction is validated in an experiment that specifies reachable sets for different regions of inputs.  },
  keywords={Machine learning, Optimization}
}

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