Optimization Learning

This article introduces the concept of optimization learning, a methodology to design optimization proxies that learn the input/output mapping of parametric optimization problems. These optimization proxies are trustworthy by design: they compute feasible solutions to the underlying optimization problems, provide quality guarantees on the returned solutions, and scale to large instances. Optimization proxies are differentiable programs that combine traditional deep learning technology with repair or completion layers to produce feasible solutions. The article shows that optimization proxies can be trained end-to-end in a self-supervised way. It presents methodologies to provide performance guarantees and to scale optimization proxies to large-scale optimization problems. The potential of optimization proxies is highlighted through applications in power systems and, in particular, real-time risk assessment and security-constrained optimal power flow.