  This paper reconsiders end-to-end learning approaches to the Optimal Power
Flow (OPF). Existing methods, which learn the input/output mapping of the OPF,
suffer from scalability issues due to the high dimensionality of the output
space. This paper first shows that the space of optimal solutions can be
significantly compressed using principal component analysis (PCA). It then
proposes Compact Learning, a new method that learns in a subspace of the
principal components before translating the vectors into the original output
space. This compression reduces the number of trainable parameters
substantially, improving scalability and effectiveness. Compact Learning is
evaluated on a variety of test cases from the PGLib with up to 30,000 buses.
The paper also shows that the output of Compact Learning can be used to
warm-start an exact AC solver to restore feasibility, while bringing
significant speed-ups.
