提出新不等式，将多任务图数据的泛化误差降至O(log n/n)
Sharper Risk Bound for Multi-Task Learning with Multi-Graph Dependent Data
- 基于新型Bennett不等式构建更紧的集中界
- 理论风险界从O(1/√n)提升至O(log n/n)
- 适合研究多任务学习与图结构数据的学者
在每个任务涉及图依赖数据的多任务学习中，现有泛化分析得到的风险界为O(1/√n)，其中n为每项任务的训练样本数。该结果次优，源于缺乏适用于多图依赖随机变量的紧致浓度不等式。本文提出一种新型Bennett型不等式，使风险界可优化至O(log n/n)。技术上，基于该不等式，构建了针对经验过程的新型Talagrand型不等式，并发展出局部分数阶Rademacher复杂度的新分析框架，从而增强多任务学习中多图依赖数据的泛化分析能力。最后，将理论成果应用于Macro-AUC优化，实验验证了其优于以往方法的优越性。
原文摘要 · Abstract (English)
In multi-task learning (MTL) with each task involving graph-dependent data, existing generalization analyses yield a \emph{sub-optimal} risk bound of $O(\frac{1}{\sqrt{n}})$, where $n$ is the number of training samples of each task. However, to improve the risk bound is technically challenging, which is attributed to the lack of a foundational sharper concentration inequality for multi-graph dependent random variables. To fill up this gap, this paper proposes a new Bennett-type inequality, enabling the derivation of a sharper risk bound of $O(\frac{\log n}{n})$. Technically, building on the proposed Bennett-type inequality, we propose a new Talagrand-type inequality for the empirical process, and further develop a new analytical framework of the local fractional Rademacher complexity to enhance generalization analyses in MTL with multi-graph dependent data. Finally, we apply the theoretical advancements to applications such as Macro-AUC optimization, illustrating the superiority of our theoretical results over prior work, which is also verified by experimental results.
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