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.

通过学习近似度度量方法，提出了一种新颖的学习优化方法，用于加速解决受限制的优化问题，对于包括广义二次规划问题在内的实际问题形式，通过不可微优化可以学习到更好的近似度度量，以增强优化算法的收敛性，并揭示了学习到的近似度度量与优化问题最优解的活动约束之间的强连接，将学习近似度度量视为一种主动集学习的形式。

度量学习加速可微参数化规划的算子分裂方法收敛