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Learning Optimal Power Flow Worst-Case Guarantees for Neural Networks

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Document pages: 7 pages

Abstract: This paper introduces for the first time a framework to obtain provableworst-case guarantees for neural network performance, using learning foroptimal power flow (OPF) problems as a guiding example. Neural networks havethe potential to substantially reduce the computing time of OPF solutions.However, the lack of guarantees for their worst-case performance remains amajor barrier for their adoption in practice. This work aims to remove thisbarrier. We formulate mixed-integer linear programs to obtain worst-caseguarantees for neural network predictions related to (i) maximum constraintviolations, (ii) maximum distances between predicted and optimal decisionvariables, and (iii) maximum sub-optimality. We demonstrate our methods on arange of PGLib-OPF networks up to 300 buses. We show that the worst-caseguarantees can be up to one order of magnitude larger than the empirical lowerbounds calculated with conventional methods. More importantly, we show that theworst-case predictions appear at the boundaries of the training input domain,and we demonstrate how we can systematically reduce the worst-case guaranteesby training on a larger input domain than the domain they are evaluated on.

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