In this paper, we investigate a problem of minimizing total energy consumption for secure federated learning (FL) over wireless edge networks. To address the high computational cost and privacy challenges in conventional FL with neural networks (NN) for resource-constrained users, we propose a novel FL with hyperdimensional computing and differential privacy (FL-HDC-DP) framework. In the considered model, each edge user employs hyperdimensional computing (HDC) for local training, which replaces complex neural updates with simple hypervector operations, and applies differential privacy (DP) noise to protect transmitted model information. We optimize the total energy of computation and communication under both latency and privacy constraints. We formulate the problem as an optimization that minimizes the total energy of all users by jointly allocating HDC dimension, transmission time, system bandwidth, transmit power, and CPU frequency. To solve this problem, a sigmoid-variant function is proposed to characterize the relationship between the HDC dimension and the convergence rounds required to reach a target accuracy. Based on this model, we develop two alternating optimization algorithms, where closed-form expressions for time, frequency, bandwidth, and power allocations are derived at each iteration. Since the iterative algorithm requires a feasible initialization, we construct a feasibility problem and obtain feasible initial resource parameters by solving a per round transmission time minimization problem. Simulation results demonstrate that the proposed FL-HDC-DP framework achieves up to 83.3% total energy reduction compared with the baseline, while attaining about 90% accuracy in approximately 3.5X fewer communication rounds than the NN baseline.

翻译：本文研究在无线边缘网络中最小化安全联邦学习（FL）总能耗的问题。针对资源受限用户采用神经网络（NN）的传统联邦学习面临的高计算成本和隐私挑战，我们提出了一种融合超维计算与差分隐私的新型联邦学习框架（FL-HDC-DP）。在该模型中，每个边缘用户采用超维计算（HDC）进行本地训练，通过简单的超向量运算替代复杂的神经网络更新，并添加差分隐私（DP）噪声以保护传输的模型信息。我们在时延和隐私约束下优化计算与通信的总能耗。将该问题建模为通过联合分配HDC维度、传输时间、系统带宽、发射功率和CPU频率以最小化所有用户总能耗的优化问题。为求解该问题，提出一种S型变体函数来刻画HDC维度与达到目标精度所需收敛轮数之间的关系。基于该模型，我们开发了两种交替优化算法，并在每次迭代中推导出时间、频率、带宽和功率分配的闭式表达式。由于迭代算法需要可行的初始值，我们构建了可行性问题，并通过求解单轮传输时间最小化问题获取可行的初始资源参数。仿真结果表明，与基线相比，所提出的FL-HDC-DP框架可实现高达83.3%的总能耗降低，同时在比NN基线少约3.5倍的通信轮数内达到约90%的准确率。