迈向建立学习型数据库操作的保证误差
Towards Establishing Guaranteed Error for Learned Database Operations
AI总结：
本文首次从理论上研究了学习型数据库操作（索引、基数估计、范围求和）的误差保证，给出了所需模型大小的下界，为模型规模与数据规模的关系提供了指导，促进了学习模型的实际应用。
摘要：
机器学习模型在各种基本数据管理操作中，包括索引（在数组中定位项目）、基数估计（估计数据库中匹配记录的数量）和范围求和估计（估计查询匹配记录的聚合属性值），已经展示了相对于非学习替代方案的显著性能提升。然而，现实世界的系统通常倾向于选择效率较低的非学习方法，因为它们能够提供（最坏情况下的）误差保证——而这正是学习方法往往欠缺的方面。这些保证的主要目标是确保系统可靠性，确保所选方法在所有数据库上始终提供所需的准确性水平。在本文中，我们首次对这些学习方法中的保证进行了理论研究，提出了使用机器学习执行索引、基数估计和范围求和估计时这些保证成立的必要条件。具体来说，我们首次提出了实现这三个关键数据库操作所需模型大小的已知下界。我们的结果界定了在给定平均和最坏情况误差下执行数据库操作所需的模型大小，作为首批理论指导方针，规定了模型大小必须如何根据数据大小变化以保证准确性水平。更广泛地说，我们建立的保证为学习模型在现实世界系统中的更广泛采用和集成铺平了道路。
英文摘要：
Machine learning models have demonstrated substantial performance enhancements over non-learned alternatives in various fundamental data management operations, including indexing (locating items in an array), cardinality estimation (estimating the number of matching records in a database), and range-sum estimation (estimating aggregate attribute values for query-matched records). However, real-world systems frequently favor less efficient non-learned methods due to their ability to offer (worst-case) error guarantees - an aspect where learned approaches often fall short. The primary objective of these guarantees is to ensure system reliability, ensuring that the chosen approach consistently delivers the desired level of accuracy across all databases. In this paper, we embark on the first theoretical study of such guarantees for learned methods, presenting the necessary conditions for such guarantees to hold when using machine learning to perform indexing, cardinality estimation and range-sum estimation. Specifically, we present the first known lower bounds on the model size required to achieve the desired accuracy for these three key database operations. Our results bound the required model size for given average and worst-case errors in performing database operations, serving as the first theoretical guidelines governing how model size must change based on data size to be able to guarantee an accuracy level. More broadly, our established guarantees pave the way for the broader adoption and integration of learned models into real-world systems.
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