Deep Initialization for Guaranteed Unimodular Quadratic Programming

In this work, we study a deep learning-based initialization approach for unimodular quadratic programs (UQPs), that are concerned with the maximization of a quadratic form over a set of complex unimodular vectors. UQPs have shown prevalent presence in many signal processing and design problems such as in wireless communications and active sensing. Stemming from their NP-hard nature, prior works on UQPs have focused on proposing approximate solutions that generally traded-off speed for obtaining theoretically sound approximations. With the aim of improving the computational efficiency of existing UQP solvers and equipped with highly-scalable deep learning frameworks as a backbone, we propose a novel hybrid solver, which we refer to as Deep-INIT. The proposed data-driven initialization approach makes use of deep learning to automatically learn "good" initializations for an underlying model-based solver called MERIT, that provides strong optimality guarantees for UQP solutions; thereby, speeding up an existing optimality-certificate producing solver for UQPs. In fact, apart from achieving a significant speed-up over the underlying UQP solver, a fundamental characteristic of Deep-INIT is that it preserves the guarantees that emerge from the model-based solver. Our numerical results reaffirm the speedup potential that Deep-INIT offers.