Reliable Projection Based Unsupervised Learning for Semi-Definite QCQP with Application of Beamforming Optimization
This work addresses a reliability issue in applying neural networks to optimization problems like beamforming, but it is incremental as it builds on existing methods to ensure feasibility.
The paper tackles the challenge of ensuring feasibility in neural network solutions for non-convex QCQP problems by proposing a reliable projection method that guarantees all outputs are feasible, with simulation results showing competitive performance against a lower bound in beamforming optimization.
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.