Reliable Projection Based Unsupervised Learning for Semi-Definite QCQP with Application of Beamforming Optimization

TL;DR

This paper introduces a reliable projection method for unsupervised neural network training in semi-definite QCQP problems, ensuring feasible solutions and improving convergence, with applications in beamforming optimization.

Contribution

It proposes a novel efficient projection technique that guarantees feasibility of NN solutions in semi-definite QCQP, enhancing convergence and performance without requiring labeled data.

Findings

Ensures all NN solutions are feasible after projection.

Improves convergence speed of neural network training.

Achieves high-quality beamforming solutions comparable to lower bounds.

Abstract

In this paper, we investigate a special class of quadratic-constrained quadratic programming (QCQP) with semi-definite constraints. Traditionally, since such a problem is non-convex and N-hard, the neural network (NN) is regarded as a promising method to obtain a high-performing solution. However, due to the inherent prediction error, it is challenging to ensure all solution output by the NN is feasible. Although some existing methods propose some naive methods, they only focus on reducing the constraint violation probability, where not all solutions are feasibly guaranteed. To deal with the above challenge, in this paper a computing efficient and reliable projection is proposed, where all solution output by the NN are ensured to be feasible. Moreover, unsupervised learning is used, so the NN can be trained effectively and efficiently without labels. Theoretically, the solution of the NN after projection is proven to be feasible, and we also prove the projection method can enhance the convergence performance and speed of the NN. To evaluate our proposed method, the quality of service (QoS)-contained beamforming scenario is studied, where the simulation results show the proposed method can achieve high-performance which is competitive with the lower bound.