用递归柯尔莫哥洛夫方法实现高效在线控制，大幅减少数据需求。
Sample-Efficient Online Control Policy Learning with Real-Time Recursive Model Updates
- 基于柯尔莫哥洛夫理论构建可实时更新的轻量级模型
- 仅需基准方法10%数据即可达成稳定控制性能
- 适合资源受限的硬件实时控制场景
数据驱动控制方法需具备高样本效率与轻量化特性，尤其在硬件上学习时数据获取与计算资源受限。现有方法多依赖大规模数据集且难以实现实时模型更新，限制了其在动态环境中的表现。柯尔莫哥洛夫理论将非线性系统形式化为可观测变量上的线性模型，可在优化友好的设置中从数据中确定，支持快速模型更新。本文提出一种高度样本高效的柯尔莫哥洛夫学习框架：递归柯尔莫哥洛夫学习（RKL）。我们明确了模型收敛的充分条件，并提供算法分析证明RKL具有轻量化与高速特性，复杂度与数据集大小无关。我们在模拟平面两连杆臂和含软执行器的混合非线性硬件系统上验证该方法，结果表明实时递归柯尔莫哥洛夫模型更新显著提升了数据驱动控制器合成的样本效率与稳定性，所需数据量不足基准方法的10%。高性能C++代码库已开源。
原文摘要 · Abstract (English)
Data-driven control methods need to be sample-efficient and lightweight, especially when data acquisition and computational resources are limited -- such as during learning on hardware. Most modern data-driven methods require large datasets and struggle with real-time updates of models, limiting their performance in dynamic environments. Koopman theory formally represents nonlinear systems as linear models over observables, and Koopman representations can be determined from data in an optimization-friendly setting with potentially rapid model updates. In this paper, we present a highly sample-efficient, Koopman-based learning pipeline: Recursive Koopman Learning (RKL). We identify sufficient conditions for model convergence and provide formal algorithmic analysis supporting our claim that RKL is lightweight and fast, with complexity independent of dataset size. We validate our method on a simulated planar two-link arm and a hybrid nonlinear hardware system with soft actuators, showing that real-time recursive Koopman model updates improve the sample efficiency and stability of data-driven controller synthesis -- requiring only <10% of the data compared to benchmarks. The high-performance C++ codebase is open-sourced. Website: https://www.zixinatom990.com/home/robotics/corl-2025-recursive-koopman-learning.
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