标题： 联邦非线性系统辨识 显示英文标题

标题： Federated Nonlinear System Identification

摘要： 我们考虑线性参数化非线性系统的联邦学习。 我们建立了联邦非线性系统识别相对于集中式方法的有效性的理论保证，证明随着客户端数量的增加，收敛速度会提高。 尽管线性和非线性情况下的收敛速率仅相差一个常数，但这个常数取决于特征映射$\phi$，在非线性情况下可以仔细选择该特征映射以增加激励并提高性能。 我们在物理环境中实验验证了我们的理论，其中客户端设备由独立同分布的控制输入和表现出独立同分布随机扰动的控制策略驱动，确保非主动探索。 实验使用来自由真实解析特征函数表征的非线性动态系统的轨迹，包括多项式和三角组件，代表了包括摆动和四旋翼动力学在内的物理系统。 我们分析了所提出方法在不同噪声水平和数据分布下的收敛行为。 结果表明，随着参与客户端数量的增加，联邦学习始终能改善任何单个客户端的收敛性。 显示英文摘要

摘要： We consider federated learning of linearly-parameterized nonlinear systems. We establish theoretical guarantees on the effectiveness of federated nonlinear system identification compared to centralized approaches, demonstrating that the convergence rate improves as the number of clients increases. Although the convergence rates in the linear and nonlinear cases differ only by a constant, this constant depends on the feature map $\phi$, which can be carefully chosen in the nonlinear setting to increase excitation and improve performance. We experimentally validate our theory in physical settings where client devices are driven by i.i.d. control inputs and control policies exhibiting i.i.d. random perturbations, ensuring non-active exploration. Experiments use trajectories from nonlinear dynamical systems characterized by real-analytic feature functions, including polynomial and trigonometric components, representative of physical systems including pendulum and quadrotor dynamics. We analyze the convergence behavior of the proposed method under varying noise levels and data distributions. Results show that federated learning consistently improves convergence of any individual client as the number of participating clients increases.