  Recent work has shown a variety of ways in which machine learning can be used
to accelerate the solution of constrained optimization problems. Increasing
demand for real-time decision-making capabilities in applications such as
artificial intelligence and optimal control has led to a variety of approaches,
based on distinct strategies. This work proposes a novel approach to learning
optimization, in which the underlying metric space of a proximal operator
splitting algorithm is learned so as to maximize its convergence rate. While
prior works in optimization theory have derived optimal metrics for limited
classes of problems, the results do not extend to many practical problem forms
including general Quadratic Programming (QP). This paper shows how
differentiable optimization can enable the end-to-end learning of proximal
metrics, enhancing the convergence of proximal algorithms for QP problems
beyond what is possible based on known theory. Additionally, the results
illustrate a strong connection between the learned proximal metrics and active
constraints at the optima, leading to an interpretation in which the learning
of proximal metrics can be viewed as a form of active set learning.
