Learning Optimal Power Flow: Worst-Case Guarantees for Neural Networks
This addresses a major barrier for adopting neural networks in practical power grid optimization by providing worst-case guarantees, though it is incremental as it builds on existing methods for a specific domain.
The paper tackles the lack of worst-case performance guarantees for neural networks in optimal power flow problems by introducing a framework using mixed-integer linear programs to provide provable bounds on constraint violations, decision errors, and sub-optimality, demonstrating on networks up to 300 buses that worst-case guarantees can be up to 10 times larger than empirical bounds and can be reduced by training on expanded input domains.
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.