DC3: A learning method for optimization with hard constraints

Abstract

Large optimization problems with hard constraints arise in many settings, yet classical solvers are often prohibitively slow, motivating the use of deep networks as cheap "approximate solvers." Unfortunately, naive deep learning approaches typically cannot enforce the hard constraints of such problems, leading to infeasible solutions. In this work, we present Deep Constraint Completion and Correction (DC3), an algorithm to address this challenge. Specifically, this method enforces feasibility via a differentiable procedure, which implicitly completes partial solutions to satisfy equality constraints and unrolls gradient-based corrections to satisfy inequality constraints. We demonstrate the effectiveness of DC3 in both synthetic optimization tasks and the real-world setting of AC optimal power flow, where hard constraints encode the physics of the electrical grid. In both cases, DC3 achieves near-optimal objective values while preserving feasibility.

In ICLR 2021. Code available at https://github.com/locuslab/DC3

References in corpus (9)

• Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• OSQP: An Operator Splitting Solver for Quadratic Programs
• Group Equivariant Convolutional Networks
• Deep Equilibrium Models
• Differentiable Convex Optimization Layers
• Task-based End-to-end Model Learning in Stochastic Optimization
• Achieving Conservation of Energy in Neural Network Emulators for Climate Modeling
• First-order Methods Almost Always Avoid Saddle Points

Cited by in corpus (11)

• Physics-Informed Neural Networks for AC Optimal Power Flow
• Characterizing possible failure modes in physics-informed neural networks
• Learning to Solve Optimization Problems with Hard Linear Constraints
• An Expandable Machine Learning-Optimization Framework to Sequential Decision-Making
• Large-scale Grid Optimization: The Workhorse of Future Grid Computations
• Model-Informed Generative Adversarial Network (MI-GAN) for Learning Optimal Power Flow
• Model-Based Domain Generalization
• Decision-Oriented Learning for Future Power System Decision-Making under Uncertainty
• Deep Learning Alternative to Explicit Model Predictive Control for Unknown Nonlinear Systems
• Approximating Solutions to the Knapsack Problem using the Lagrangian Dual Framework
• Towards Understanding the Unreasonable Effectiveness of Learning AC-OPF Solutions