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Prior work has successfully incorporated optimization layers as the lastlayer in neural networks for various problems, thereby allowing joint learningand planning in one neural network forward pass. In this work, we identify aweakness in such a set-up where inputs to the optimization layer lead toundefined output of the neural network. Such undefined decision outputs canlead to possible catastrophic outcomes in critical real time applications. Weshow that an adversary can cause such failures by forcing rank deficiency onthe matrix fed to the optimization layer which results in the optimizationfailing to produce a solution. We provide a defense for the failure cases bycontrolling the condition number of the input matrix. We study the problem inthe settings of synthetic data, Jigsaw Sudoku, and in speed planning forautonomous driving, building on top of prior frameworks in end-to-end learningand optimization. We show that our proposed defense effectively prevents theframework from failing with undefined output. Finally, we surface a number ofedge cases which lead to serious bugs in popular equation and optimizationsolvers which can be abused as well.

Beyond NaN: Resiliency of Optimization Layers in The Face of Infeasibility