High-speed batch processing of semidefinite programs with feedforward neural networks

Semidefinite programming is an important optimization task, often used in time-sensitive applications. Though they are solvable in polynomial time, in practice they can be too slow to be used in online, i.e. real-time applications. Here we propose to solve feasibility semidefinite programs using artificial neural networks (NNs). Given the optimization constraints as an input, a NN outputs values for the optimization parameters such that the constraints are satisfied, both for the primal and the dual formulations of the task. We train the network without having to exactly solve the semidefinite program even once, thus avoiding the possibly time-consuming task of having to generate many training samples with conventional solvers. The NN method is only inconclusive if both the primal and dual models fail to provide feasible solutions. Otherwise we always obtain a certificate, which guarantees false positives to be excluded. As a proof-of-principle demonstration, we examine the performance of the method on a hierarchy of quantum information tasks, the Navascues-Pironio-Acin hierarchy applied to the Bell scenario. We demonstrate that the trained NN gives decent accuracy, while showing orders of magnitude increase in speed compared to a traditional solver, once trained. The network does not have to be retrained for similarly structured problems, giving the promise for being a fast solver for these types of problems.

Automated summary

The proposed method uses artificial neural networks to solve feasibility semidefinite programs, achieving decent accuracy and orders of magnitude increase in speed compared to traditional solvers for quantum information tasks.