Tracking Moving Agents via Inexact Online Gradient Descent Algorithm

Multiagent systems are being increasingly deployed in challenging environments for performing complex tasks such as multitarget tracking, search-and-rescue, and intrusion detection. Not with standing the computational limitations of individual robots, such systems rely on collaboration to sense and react to the environment. This paper formulates the generic target tracking problem as a time-varying optimization problem and puts forth an inexact online gradient descent method for solving it sequentially. The performance of the proposed algorithm is studied by characterizing its dynamic regret, a notion common to the online learning literature. Building upon the existing results, we provide improved regret rates that not only allow nonstrongly convex costs but also explain the role of the cumulative gradient error. Two distinct classes of problems are considered: one in which the objective function adheres to a quadratic growth condition, and another where the objective function is convex but the variable belongs to a compact domain. For both cases, results are developed while allowing the error to be either adversarial or arising from a white noise process. Further, the generality of the proposed framework is demonstrated by developing online variants of existing stochastic gradient algorithms and interpreting them as special cases of the proposed inexact gradient method. The efficacy of the proposed inexact gradient framework is established on a multiagent multitarget tracking problem, while its flexibility is exemplified by generating online movie recommendations for Movielens 10M dataset.