Differentiable Projection-based Learn to Optimize in Wireless Network-Part I: Convex Constrained (Non-)Convex Programming

TL;DR

This paper introduces a projection-based neural network approach for solving convex and non-convex constrained optimization problems in wireless networks, ensuring feasibility and enabling unsupervised training.

Contribution

It proposes a novel projection-based method that guarantees feasible solutions from neural networks and derives gradients for label-free training in constrained optimization.

Findings

Ensures feasibility of NN solutions via projection

Enables unsupervised training through gradient derivation

Outperforms traditional methods in constrained optimization tasks

Abstract

This paper addresses a class of (non-)convex optimization problems subject to general convex constraints, which pose significant challenges for traditional methods due to their inherent non-convexity and diversity. Conventional convex optimization-based solvers often struggle to efficiently handle these problems in their most general form. While neural network (NN)-based approaches offer a promising alternative, ensuring the feasibility of NN-generated solutions and effectively training the NN remain key hurdles, largely because finite-capacity networks can produce infeasible outputs. To overcome these issues, we propose a projection-based method that projects any infeasible NN output onto the feasible domain, thus guaranteeing strict adherence to the constraints without compromising the NN's optimization capability. Furthermore, we derive the objective function values for both the raw NN outputs and their projected counterparts, along with the gradients of these values with respect to the NN parameters. This derivation enables label-free (unsupervised) training, reducing reliance on labeled data and improving scalability. Experimental results demonstrate that the proposed projection-based method consistently ensures feasibility.