Shih Yu Chang

Shih-Yu Chang

This paper addresses the advancement of probability tail bound analysis, a crucial statistical tool for assessing the probability of large deviations of random variables from their expected values. Traditional tail bounds, such as Markov's, Chebyshev's, and Chernoff bounds, have proven valuable across numerous scientific and engineering fields. However, as data complexity grows, there is a pressing need to extend tail bound estimation from scalar variables to high-dimensional random objects. Existing studies often rely on the assumption of independence among high-dimensional random objects, an assumption that may not always be valid. Building on the work of researchers like Garg et al. and Chang, who employed random walks to model high-dimensional ensembles, this study introduces a more generalized approach by exploring random walks over manifolds. To address the challenges of constructing an appropriate underlying graph for a manifold, we propose a novel method that enhances random walks on graphs approximating the manifold. This approach ensures spectral similarity between the original manifold and the approximated graph, including matching eigenvalues, eigenvectors, and eigenfunctions. Leveraging graph approximation technique proposed by Burago et al. for manifolds, we derive the tensor Chernoff bound and establish its range for random walks on a Riemannian manifold according to the underlying manifold's spectral characteristics.

Lijie Zheng, Ji He, Shih Yu Chang et al.

This work tackles the physical layer security (PLS) problem of maximizing the secrecy rate in heterogeneous UAV networks (HetUAVNs) under propulsion energy constraints. Unlike prior studies that assume uniform UAV capabilities or overlook energy-security trade-offs, we consider a realistic scenario where UAVs with diverse payloads and computation resources collaborate to serve ground terminals in the presence of eavesdroppers. To manage the complex coupling between UAV motion and communication, we propose a hierarchical optimization framework. The inner layer uses a semidefinite relaxation (SDR)-based S2DC algorithm combining penalty functions and difference-of-convex (d.c.) programming to solve the secrecy precoding problem with fixed UAV positions. The outer layer introduces a Large Language Model (LLM)-guided heuristic multi-agent reinforcement learning approach (LLM-HeMARL) for trajectory optimization. LLM-HeMARL efficiently incorporates expert heuristics policy generated by the LLM, enabling UAVs to learn energy-aware, security-driven trajectories without the inference overhead of real-time LLM calls. The simulation results show that our method outperforms existing baselines in secrecy rate and energy efficiency, with consistent robustness across varying UAV swarm sizes and random seeds.