Optimization Learning

TL;DR

Optimization learning fuses deep learning with differentiable repair/completion layers to learn fast, feasible mappings for parametric optimization problems. It presents primal optimization proxies, dual optimization proxies, and primal-dual learning to produce feasible solutions and reliable bounds, trained end-to-end in a self-supervised or supervised manner. Demonstrations on power-system tasks—Economic Dispatch with reserves and Security-Constrained OPF—show orders-of-magnitude speedups with competitive or superior feasibility and optimality guarantees compared with traditional solvers and baselines. The results indicate real-time risk assessment and large-scale operational planning become feasible, while pointing to open directions for repair-layer design, combinatorial optimization, and broader optimization domains.

Abstract

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.

Figures (10)

• Figure 1: The Training of Supervised Learning Models.
• Figure 2: The Architecture of Optimization Proxies.
• Figure 3: End to End Training of Optimization Proxies.
• Figure 4: Explicit versus Implicit Layers in Deep Learning.
• Figure 5: The Optimization Proxy for the Economic Dispatch Problem (adapted from E2ELR).