  Learning to optimize (L2O) is an emerging approach that leverages machine
learning to develop optimization methods, aiming at reducing the laborious
iterations of hand engineering. It automates the design of an optimization
method based on its performance on a set of training problems. This data-driven
procedure generates methods that can efficiently solve problems similar to
those in the training. In sharp contrast, the typical and traditional designs
of optimization methods are theory-driven, so they obtain performance
guarantees over the classes of problems specified by the theory. The difference
makes L2O suitable for repeatedly solving a certain type of optimization
problems over a specific distribution of data, while it typically fails on
out-of-distribution problems. The practicality of L2O depends on the type of
target optimization, the chosen architecture of the method to learn, and the
training procedure. This new paradigm has motivated a community of researchers
to explore L2O and report their findings.
  This article is poised to be the first comprehensive survey and benchmark of
L2O for continuous optimization. We set up taxonomies, categorize existing
works and research directions, present insights, and identify open challenges.
We also benchmarked many existing L2O approaches on a few but representative
optimization problems. For reproducible research and fair benchmarking
purposes, we released our software implementation and data in the package
Open-L2O at https://github.com/VITA-Group/Open-L2O.
