Distributed Byzantine-Resilient Learning of Multi-UAV Systems via Filter-Based Centerpoint Aggregation Rules

Dear Editor, Through distributed machine learning, multi-UAV systems can achieve global optimization goals without a centralized server, such as optimal target tracking, by leveraging local calculation and communication with neighbors. In this work, we implement the stochastic gradient descent algorithm (SGD) distributedly to optimize tracking errors based on local state and aggregation of the neighbors' estimation. However, Byzantine agents can mislead neighbors, causing deviations from optimal tracking. We prove that the swarm achieves resilient convergence if aggregated results lie within the normal neighbors' convex hull, which can be guaranteed by the introduced centerpoint-based aggregation rule. In the given simulated scenarios, distributed learning using average, geometric median (GM), and coordinate-wise median (CM) based aggregation rules fail to track the target. Compared to solely using the centerpoint aggregation method, our approach, which combines a pre-filter with the centroid aggregation rule, significantly enhances resilience against Byzantine attacks, achieving faster convergence and smaller tracking errors.