[论文解读] K-Regret Queries: From Additive to Multiplicative Utilities.

Jianzhong Qi, Fei Zuo+1 more|arXiv (Cornell University)|Sep 26, 2016

Data Management and Algorithms参考文献 23被引用 3

一句话总结

本文提出了首个针对乘法效用函数（如Cobb-Douglas函数和常替代弹性（CES）函数）的k-后悔查询算法，实现了有界的后悔比率。该研究将k-后悔查询理论从加法效用扩展至乘法效用，实现了无需预先指定用户效用函数即可高效且低后悔地处理查询。

ABSTRACT

The k-regret queries aim to return a size-k subset of the entire database such that, for any query user that selects a data object in this size-k subset rather than in the entire database, her is minimized. Here, the regret ratio is modeled by the level of difference in the optimality between the optimal object in the size-k subset returned and the optimal object in the entire database. The optimality of a data object in turn is usually modeled by a utility function of the query user. Compared with traditional top-k queries, the k-regret queries have the advantage of not requiring the users to specify their utility functions. The k-regret queries can discover a size-k subset that minimizes the regret ratio for a whole family of utility functions without knowing any particular of them. Previous studies have answered k-regret queries with additive utility functions such as the linear summation function. However, no existing result has been reported to answer k-regret queries with multiplicative utility functions, which are an important family of utility functions. In this study, we break the barrier of multiplicative utility functions. We present an algorithm that can produce answers with a bounded regret ratio to k-regret queries with multiplicative utility functions. As a case study we apply this algorithm to process a special type of multiplicative utility functions, the Cobb-Douglas function, and a closely related function, the Constant Elasticity of Substitution function. We perform extensive experiments on the proposed algorithm. The results confirm that the proposed algorithm can answer the k-regret queries with multiplicative utility functions efficiently with a constantly low regret ratio.

研究动机与目标

• 为解决在经济学和决策制定中常见的乘法效用函数下k-后悔查询处理的空白。
• 设计一种算法，确保在乘法效用模型下k-后悔查询的后悔比率有界。
• 将k-后悔查询的适用范围从加法效用函数扩展至现实场景中更广泛的效用函数类别。
• 在合成数据集和真实数据集上评估所提算法的性能和后悔比率。
• 展示该算法在极少用户偏好指定条件下，处理乘法效用函数时的高效性与有效性。

提出的方法

• 提出一种新颖算法，将乘法效用函数转换为适用于k-后悔查询处理的等价形式。
• 利用几何与优化技术，识别出大小为k的子集，以最小化在该类效用函数族中所有可能效用函数的最大后悔比率。
• 聚焦于两类关键的乘法效用族：Cobb-Douglas函数与常替代弹性（CES）函数。
• 通过效用空间的变换，将乘法后悔最小化问题转化为可处理的优化问题。
• 采用采样与剪枝策略，高效探索候选结果集，同时保持后悔比率的边界。
• 将算法集成至查询处理管道中，支持动态用户偏好，且无需显式输入效用函数。

实验结果

研究问题

• RQ1 k-后悔查询能否在Cobb-Douglas函数和CES函数等乘法效用函数下被有效回答？
• RQ2 在乘法效用下，k-后悔查询算法可实现的理论后悔比率边界是多少？
• RQ3 与基于加法效用的现有k-后悔查询方法相比，所提算法在效率和后悔比率方面表现如何？
• RQ4 该算法能否在各类不同的效用函数族中保持一致的低后悔比率？
• RQ5 该算法在真实世界和合成数据集上的可扩展性与性能表现如何？

主要发现

• 所提算法在Cobb-Douglas函数和CES函数等乘法效用函数下，实现了k-后悔查询的有界后悔比率。
• 在各种数据集和效用函数参数下，后悔比率始终保持极低，表现出强健性。
• 该算法高效处理查询，且无需用户预先指定其效用函数。
• 大量实验验证了该算法在合成数据和真实数据上的高效性与低后悔比率。
• 该方法成功将k-后悔查询理论从加法效用扩展至乘法效用函数，填补了偏好感知查询处理中的关键空白。
• 在后悔比率方面，该算法优于基线方法，同时保持了可扩展的性能。