学习最优潮流：神经网络的最坏情况保证
Learning Optimal Power Flow: Worst-Case Guarantees for Neural Networks
摘要：
本文首次介绍了一个框架，以获得可证明的最坏情况下的保证神经网络的性能，学习最优潮流（OPF）问题作为指导性的例子。神经网络有可能大大减少OPF解决方案的计算时间。然而，缺乏对最坏情况下性能的保证仍然是实际采用的主要障碍。这项工作旨在消除这一障碍。我们制定混合整数线性规划，以获得最坏情况下的保证神经网络预测有关（i）最大约束违反，（ii）预测和最佳决策变量之间的最大距离，和（iii）最大次优。我们展示了我们的方法在一系列的PGLib-OPF网络高达300总线。我们表明，最坏情况下的保证可以高达一个数量级大于传统方法计算的经验下限。更重要的是，我们证明了最坏情况的预测出现在训练输入域的边界处，并且我们演示了如何通过在比它们被评估的域更大的输入域上进行训练来系统地减少最坏情况的保证。
英文摘要：
This paper introduces for the first time a framework to obtain provable worst-case guarantees for neural network performance, using learning for optimal power flow (OPF) problems as a guiding example. Neural networks have the potential to substantially reduce the computing time of OPF solutions. However, the lack of guarantees for their worst-case performance remains a major barrier for their adoption in practice. This work aims to remove this barrier. We formulate mixed-integer linear programs to obtain worst-case guarantees for neural network predictions related to (i) maximum constraint violations, (ii) maximum distances between predicted and optimal decision variables, and (iii) maximum sub-optimality. We demonstrate our methods on a range of PGLib-OPF networks up to 300 buses. We show that the worst-case guarantees can be up to one order of magnitude larger than the empirical lower bounds calculated with conventional methods. More importantly, we show that the worst-case predictions appear at the boundaries of the training input domain, and we demonstrate how we can systematically reduce the worst-case guarantees by training on a larger input domain than the domain they are evaluated on.
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