2020/07/10 by Kamil Nar, Yuan Xue, Nar, Kamil +3 · 1 citation
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2007.05189
openalex publication_date 2020/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.