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 setting respectively.

翻译：我们研究在底层演化函数未知的情况下，学习预测动力系统下一状态的问题。与以往工作不同，我们对动力系统不施加任何参数化假设，而是从学习理论视角研究该问题。我们定义了新的组合测度和维度，并证明它们分别量化了可实现场景与不可知场景下的最优错误界和遗憾界。