论文标题
超越NAN:面对不可行的优化层的弹性
Beyond NaN: Resiliency of Optimization Layers in The Face of Infeasibility
论文作者
论文摘要
先前的工作已成功地将优化层作为神经网络中的最后一层,以解决各种问题,从而可以在一个神经网络向前通行中进行联合学习和计划。在这项工作中,我们确定了这种设置中的弱点,其中对优化层的输入导致神经网络的不确定输出。这种不确定的决策输出可以导致关键实时应用中可能的灾难性结果。我们表明,对手会通过强迫进食矩阵上的等级缺陷到优化层,从而导致优化层,从而导致优化无法产生解决方案。我们通过控制输入矩阵的条件数来为故障情况提供防御。我们在合成数据,拼图Sudoku的设置以及自动驾驶的速度计划中研究了问题,在端到端学习和优化的先前框架之上。我们表明,我们提出的防御有效地阻止了框架未定义的输出失败。最后,我们浮出了许多边缘案例,这些案例会导致流行方程式和优化求解器中的严重错误,这也可以滥用。
Prior work has successfully incorporated optimization layers as the last layer in neural networks for various problems, thereby allowing joint learning and planning in one neural network forward pass. In this work, we identify a weakness in such a set-up where inputs to the optimization layer lead to undefined output of the neural network. Such undefined decision outputs can lead to possible catastrophic outcomes in critical real time applications. We show that an adversary can cause such failures by forcing rank deficiency on the matrix fed to the optimization layer which results in the optimization failing to produce a solution. We provide a defense for the failure cases by controlling the condition number of the input matrix. We study the problem in the settings of synthetic data, Jigsaw Sudoku, and in speed planning for autonomous driving, building on top of prior frameworks in end-to-end learning and optimization. We show that our proposed defense effectively prevents the framework from failing with undefined output. Finally, we surface a number of edge cases which lead to serious bugs in popular equation and optimization solvers which can be abused as well.