Learning Unstable Dynamical Systems with Time-Weighted Logarithmic Loss
arxiv(2020)
摘要
When training the parameters of a linear dynamical model, the gradient descent algorithm is likely to fail to converge if the squared-error loss is used as the training loss function. Restricting the parameter space to a smaller subset and running the gradient descent algorithm within this subset can allow learning stable dynamical systems, but this strategy does not work for unstable systems. In this work, we look into the dynamics of the gradient descent algorithm and pinpoint what causes the difficulty of learning unstable systems. We show that observations taken at different times from the system to be learned influence the dynamics of the gradient descent algorithm in substantially different degrees. We introduce a time-weighted logarithmic loss function to fix this imbalance and demonstrate its effectiveness in learning unstable systems.
更多查看译文
关键词
unstable dynamical systems,learning,time-weighted
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络