Deep Learning-Aided Unimodular Quadratic Programming:Initialization and Provable Guarantees

In this thesis, we study an important optimization problem called “Unimodular Quadratic Program” (UQP) that has shown its presence in prominent applications such as wireless communication, active sensing, etc. UQP is an NP-hard constrained optimization problem and prior works that have proposed approximate solutions have generally suffered from the speed versus reliability trade-off. With the aim to improve the computational efficiency of existing UQP solutions and equipped with the highly scalable deep learning framework as a backbone, we propose two novel solvers for UQP. Our first solution is a black-box computational approach, which we call Deep-PMLI, where the deep learning model learns to predict a solution to a given UQP based on already seen example UQPs. Deep-PMLI is an attractive solver for applications that require low-cost solutions but do not require strong guarantees. In our second solution, Deep-INIT, we propose a novel data-driven strategy to speed-up an existing provably optimal solver for UQP. Deep-INIT, apart from achieving a significant speed-up over the underlying UQP solver, also preserves its guarantees.