Universal Learning of Nonlinear Dynamics
Evan Dogariu, Anand Brahmbhatt and Elad Hazan
我们研究了学习临界稳定未知非线性动力系统的基本问题。我们基于谱滤波技术描述了一种算法，该算法通过系统的谱表示，学习从过去观测到下一个观测的映射。利用在线凸优化技术，我们证明了对于任何具有有限多个临界稳定模态的非线性动力系统，预测误差都会消失，其速率由一种新颖的定量控制理论可学习性概念所决定。我们方法的主要技术组成部分是一种新的线性动力系统谱滤波算法，该算法结合了过去观测并适用于一般的噪声和临界稳定系统。这显著地将原始谱滤波算法推广到非对称动力学以及包含噪声校正的情况，具有独立的研究价值。
We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to the next based on a spectral representation of the system. Using techniques from online convex optimization, we prove vanishing prediction error for any nonlinear dynamical system that has finitely many marginally stable modes, with rates governed by a novel qu...