提出轻量通信的联邦学习算法，实现异构智能体高效协同控制。
Scalar Federated Learning for Linear Quadratic Regulator
- 每轮仅上传一个标量，大幅降低通信开销
- 参与设备越多，梯度恢复越准，收敛更快
- 适合大规模分布式控制场景，尤其高维系统
我们提出 ScalarFedLQR，一种面向异构智能体线性二次型调节器（LQR）控制的模型无关联邦学习算法。该方法基于分解投影梯度机制，各智能体仅需上传局部零阶梯度估计的一个标量投影。服务器通过聚合这些标量信息重建全局下降方向，将每智能体上行通信量从 O(d) 降至 O(1)，与策略维度无关。关键的是，投影引起的近似误差随参与智能体数量增加而减小，形成有利的缩放规律：更大规模群体可实现更精确的梯度恢复，允许更大的步长，并在高维情况下仍保持快速线性收敛。在标准正则条件下，所有迭代解均保持稳定，平均 LQR 代价以线性速度下降。数值实验表明，该方法性能接近全梯度联邦 LQR，但通信开销显著降低。
原文摘要 · Abstract (English)
We propose ScalarFedLQR, a communication-efficient federated algorithm for model-free learning of a common policy in linear quadratic regulator (LQR) control of heterogeneous agents. The method builds on a decomposed projected gradient mechanism, in which each agent communicates only a scalar projection of a local zeroth-order gradient estimate. The server aggregates these scalar messages to reconstruct a global descent direction, reducing per-agent uplink communication from O(d) to O(1), independent of the policy dimension. Crucially, the projection-induced approximation error diminishes as the number of participating agents increases, yielding a favorable scaling law: larger fleets enable more accurate gradient recovery, admit larger stepsizes, and achieve faster linear convergence despite high dimensionality. Under standard regularity conditions, all iterates remain stabilizing and the average LQR cost decreases linearly fast. Numerical results demonstrate performance comparable to full-gradient federated LQR with substantially reduced communication.
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