This paper provides statistical guarantees on the accuracy of dynamical models learned from dependent data sequences. Specifically, we develop uniform error bounds that apply to quantized models and imperfect optimization algorithms commonly used in practical contexts for system identification, and in particular hybrid system identification. Two families of bounds are obtained: slow-rate bounds via a block decomposition and fast-rate, variance-adaptive, bounds via a novel spaced-point strategy. The bounds scale with the number of bits required to encode the model and thus translate hardware constraints into interpretable statistical complexities.

翻译：本文为从相关数据序列中学习的动态模型的准确性提供了统计保证。具体而言，我们建立了适用于量化模型及实际系统辨识（特别是混合系统辨识）中常用非完美优化算法的均匀误差界。我们获得了两种类型的界：通过块分解得到的慢速收敛界，以及通过一种新颖的间隔点策略得到的快速收敛、方差自适应的界。这些界随编码模型所需的比特数而变化，从而将硬件约束转化为可解释的统计复杂度。