DC3: A learning method for optimization with hard constraints

TL;DR

DC3 is a novel deep learning approach that efficiently enforces hard constraints in large optimization problems, ensuring feasible solutions with near-optimal objectives in both synthetic and real-world applications.

Contribution

The paper introduces DC3, a differentiable method that completes and corrects partial solutions to satisfy complex equality and inequality constraints in optimization.

Findings

DC3 achieves near-optimal solutions in synthetic tasks.

DC3 maintains feasibility in AC power flow problems.

DC3 outperforms naive deep learning approaches in constrained optimization.

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.