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On the Surprising Effectiveness of Spectrum Clipping in Learning Stable Linear Dynamics
🤖 AI Summary
Balancing accuracy, stability, and computational efficiency remains challenging in learning linear dynamical systems. This paper proposes Spectral Clipping (SC): first fitting a linear system unconstrainedly, then clipping all eigenvalues of the system matrix with magnitude greater than one to exactly one via eigendecomposition. We provide the first theoretical guarantee that this simple post-processing ensures strict closed-loop stability while preserving high predictive accuracy and incurring negligible computational overhead. SC is further extended to Koopman-based nonlinear modeling and robust policy learning from unstable demonstrations. On multiple benchmark datasets, SC significantly outperforms strong baselines—accelerating training by several orders of magnitude—while successfully modeling complex, stable nonlinear dynamics such as multi-finger dexterous manipulation. Moreover, it exhibits strong robustness to failed or truncated demonstrations.
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Application Category
📝 Abstract
When learning stable linear dynamical systems from data, three important properties are desirable: i) predictive accuracy, ii) provable stability, and iii) computational efficiency. Unconstrained minimization of reconstruction errors leads to high accuracy and efficiency but cannot guarantee stability. Existing methods to remedy this focus on enforcing stability while also ensuring accuracy, but do so only at the cost of increased computation. In this work, we investigate if a straightforward approach can simultaneously offer all three desiderata of learning stable linear systems. Specifically, we consider a post-hoc approach that manipulates the spectrum of the learned system matrix after it is learned in an unconstrained fashion. We call this approach spectrum clipping (SC) as it involves eigen decomposition and subsequent reconstruction of the system matrix after clipping all of its eigenvalues that are larger than one to one (without altering the eigenvectors). Through detailed experiments involving two different applications and publicly available benchmark datasets, we demonstrate that this simple technique can simultaneously learn highly accurate linear systems that are provably stable. Notably, we demonstrate that SC can achieve similar or better performance than strong baselines while being orders-of-magnitude faster. We also show that SC can be readily combined with Koopman operators to learn stable nonlinear dynamics, such as those underlying complex dexterous manipulation skills involving multi-fingered robotic hands. Further, we find that SC can learn stable robot policies even when the training data includes unsuccessful or truncated demonstrations. Our codes and dataset can be found at https://github.com/GT-STAR-Lab/spec_clip.
Problem
Research questions and friction points this paper is trying to address.
Accuracy
Stability
Efficient Computation
Innovation
Methods, ideas, or system contributions that make the work stand out.
Spectral Clipping
Linear Dynamical Systems
Stable Robotics Learning
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