Tracking Moving Agents via Inexact Online Gradient Descent Algorithm

TL;DR

This paper introduces an inexact online gradient descent algorithm for tracking moving agents in multi-agent systems, providing improved regret bounds and demonstrating its effectiveness on tracking and recommendation tasks.

Contribution

It proposes a novel inexact online gradient descent method with enhanced regret analysis for time-varying optimization in multi-agent tracking, accommodating non-strongly convex costs and gradient errors.

Findings

Improved regret rates for non-strongly convex functions.

Effective multi-agent multi-target tracking results.

Versatility demonstrated through online movie recommendation.

Abstract

Multi-agent systems are being increasingly deployed in challenging environments for performing complex tasks such as multi-target tracking, search-and-rescue, and intrusion detection. Notwithstanding 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 non-strongly convex costs but also explicating 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 multi-agent multi-target tracking problem, while its flexibility is exemplified by generating online movie recommendations for Movielens $10$M dataset.