The identification of optimal structures within vast arrays of interconnected data necessitates significant sampling- and computational effort. Learning and leveraging underlying signal dependencies can improve efficiency and predictive capabilities considerably, but the ubiquity of nonlinear statistical relations amplifies the complexity of such undertakings. In this paper, we develop novel generic and adaptive strategies equipped with routines for graph-based causal reward modeling, analytic reproducing kernel methods, and Taylor approximation of functional processes. We establish theoretical performance guarantees sublinear in time and linear in data volume over time. Our analyses cover robustness to a multitude of uncertainties arising from noise interference, gradual model convergence, and solution space mismatch. The framework's general appeal is substantiated by a minimalistic set of conditions or reliance on prior estimates, while various outlined modifications address specific or extended settings. To demonstrate practical effectiveness, we conduct numerical experiments using both benchmarked synthetic and real-world transportation datasets.

翻译：摘要：在互连数据构成的庞大阵列中识别最优结构需要大量采样和计算成本。学习并利用底层信号依赖关系可显著提升效率和预测能力，但非线性统计关系的普遍存在加剧了此类任务的复杂性。本文开发了配备图基因果奖励建模、分析再生核方法与函数过程泰勒逼近等机制的新型通用自适应策略。我们建立了随时间呈次线性增长、随数据量呈线性增长的理论性能保证。相关分析涵盖了对噪声干扰、模型渐进收敛及解空间失配等多重不确定性的鲁棒性。该框架的普适性通过极简的条件设定或对先验估计的依赖得以彰显，同时提出的多种改进方案针对特定或扩展场景进行了适配。为验证实践有效性，我们利用基准合成数据集与真实交通运输数据集开展了数值实验。