The Complexity of Sequential Prediction in Dynamical Systems
Abstract
We study the problem of learning to predict the next state of a dynamical system when the underlying evolution function is unknown. Unlike previous work, we place no parametric assumptions on the dynamical system, and study the problem from a learning theory perspective. We define new combinatorial measures and dimensions and show that they quantify the optimal mistake and regret bounds in the realizable and agnostic settings respectively. By doing so, we find that in the realizable setting, the total number of mistakes can grow according to \emph{any} increasing function of the time horizon $T$. In contrast, we show that in the agnostic setting under the commonly studied notion of Markovian regret, the only possible rates are $\Theta(T)$ and $\tilde{\Theta}(\sqrt{T})$.
Cite
Text
Raman et al. "The Complexity of Sequential Prediction in Dynamical Systems." Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, 2025.Markdown
[Raman et al. "The Complexity of Sequential Prediction in Dynamical Systems." Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, 2025.](https://mlanthology.org/l4dc/2025/raman2025l4dc-complexity/)BibTeX
@inproceedings{raman2025l4dc-complexity,
title = {{The Complexity of Sequential Prediction in Dynamical Systems}},
author = {Raman, Vinod and Subedi, Unique and Tewari, Ambuj},
booktitle = {Proceedings of the 7th Annual Learning for Dynamics \& Control Conference},
year = {2025},
pages = {124-138},
volume = {283},
url = {https://mlanthology.org/l4dc/2025/raman2025l4dc-complexity/}
}