Scaling Submodular Optimization Approaches for Control Applications in Networked Systems

Abstract: Often times, in many design problems, there is a need to select a small set of informative or representative elements from a large ground set of entities in an optimal fashion. Submodular optimization that provides for a formal way to solve such problems, has recently received significant attention from the controls community where such subset selection problems are abound. However, scaling these approaches to large systems can be challenging because of the high computational complexity of the overall flow, in-part due to the high-complexity compute-oracles used to determine the objective function values. In this work, we explore a well-known paradigm, namely leader-selection in a multi-agent networked environment to illustrate strategies for scalable submodular optimization. We study the performance of the state-of-the-art stochastic and distributed greedy algorithms as well as explore techniques that accelerate the computation oracles within the optimization loop. We finally present results combining accelerated greedy algorithms with accelerated computation oracles and demonstrate significant speedups with little loss of optimality when compared to the baseline ordinary greedy algorithm.