An Optimization Framework for Certain Separable Problems using Neural Networks

This paper studies a class of parametric constrained optimization problems that are motivated by applications in real time applications. Under a parameter-separable problem structure that naturally arises in these applications, the paper proposes a two phase strategy, based on offline learning and online processing, to address these optimization problems on resource limited devices. Specifically, by exploiting the separable structure, an iterative Alternating Direction Method of Multipliers (ADMM) based solution procedure is developed that enables the use of certain learning based function representations (learned offline but readily computable online) to reduce the overall online on-device implementation complexity. By carefully crafting the ADMM procedure, it is shown that even as the parameters vary, the corresponding instances of the parametric optimization problem may be solved by lightweight online computations in the device with the assistance of a neural network co-processor.