  Leveraging machine learning to facilitate the optimization process is an
emerging field that holds the promise to bypass the fundamental computational
bottleneck caused by classic iterative solvers in critical applications
requiring near-real-time optimization. The majority of existing approaches
focus on learning data-driven optimizers that lead to fewer iterations in
solving an optimization. In this paper, we take a different approach and
propose to replace the iterative solvers altogether with a trainable parametric
set function, that outputs the optimal arguments/parameters of an optimization
problem in a single feed forward. We denote our method as Learning to Optimize
the Optimization Process (LOOP). We show the feasibility of learning such
parametric (set) functions to solve various classic optimization problems
including linear/nonlinear regression, principal component analysis,
transport-based coreset, and quadratic programming in supply management
applications. In addition, we propose two alternative approaches for learning
such parametric functions, with and without a solver in the LOOP. Finally,
through various numerical experiments, we show that the trained solvers could
be orders of magnitude faster than the classic iterative solvers while
providing near optimal solutions.
