Unrolled Neural Networks for Constrained Optimization

TL;DR

This paper introduces a novel neural network framework called constrained dual unrolling (CDU) that learns to solve constrained optimization problems efficiently, generalizing well to new data and providing near-optimal solutions.

Contribution

The paper develops a new unrolled neural network approach that incorporates primal-dual dynamics for constrained optimization, with a novel training procedure for improved generalization.

Findings

Achieves near-optimal solutions for MIQPs and power allocation.

Exhibits strong out-of-distribution generalization.

Provides a learnable, accelerated alternative to dual ascent algorithms.

Abstract

In this paper, we develop unrolled neural networks to solve constrained optimization problems, offering accelerated, learnable counterparts to dual ascent (DA) algorithms. Our framework, termed constrained dual unrolling (CDU), comprises two coupled neural networks that jointly approximate the saddle point of the Lagrangian. The primal network emulates an iterative optimizer that finds a stationary point of the Lagrangian for a given dual multiplier, sampled from an unknown distribution. The dual network generates trajectories towards the optimal multipliers across its layers while querying the primal network at each layer. Departing from standard unrolling, we induce DA dynamics by imposing primal-descent and dual-ascent constraints through constrained learning. We formulate training the two networks as a nested optimization problem and propose an alternating procedure that updates the primal and dual networks in turn, mitigating uncertainty in the multiplier distribution required for primal network training. We numerically evaluate the framework on mixed-integer quadratic programs (MIQPs) and power allocation in wireless networks. In both cases, our approach yields near-optimal near-feasible solutions and exhibits strong out-of-distribution (OOD) generalization.