ニューラルKoopman演算子のスケーリング則
Scaling Law of Neural Koopman Operators
データ駆動型ニューラルKoopman演算子のサンプル数・潜在次元・制御性能の関係をスケーリング則として定式化し、2つの正則化で制御性能を改善した研究。
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著者: Abulikemu Abuduweili, Yuyang Pang, Feihan Li, Changliu Liu
分類: cs.RO
原文アブストラクト
Data-driven neural Koopman operator theory has emerged as a powerful tool for linearizing and controlling nonlinear robotic systems. However, the performance of these data-driven models fundamentally depends on the trade-off between sample size and model dimensions, a relationship for which the scaling laws have remained unclear. This paper establishes a rigorous framework to address this challenge by deriving and empirically validating scaling laws that connect sample size, latent space dimension, and downstream control quality. We derive a theoretical upper bound on the Koopman approximation error, explicitly decomposing it into sampling error and projection error. We show that these terms decay at specific rates relative to dataset size and latent dimension, providing a rigorous basis for the scaling law. Based on the theoretical results, we introduce two lightweight regularizers for the neural Koopman operator: a covariance loss to help stabilize the learned latent features and an inverse control loss to ensure the model aligns with physical actuation. The results from systematic experiments across six robotic environments confirm that model fitting error follows the derived scaling laws, and the regularizers improve dynamic model fitting fidelity, with enhanced closed-loop control performance. Together, our results provide a simple recipe for allocating effort between data collection and model capacity when learning Koopman dynamics for control.
関連論文
- 非線形システム制御のための深層Koopmanオペレータ制御/モデル学習
