The k -regret query aims to return a size- k subset S of a database D such that, for any query user that selects a data object from this size- k subset S rather than from database D , her regret ratio is minimized. The regret ratio here is modeled by the relative difference in the optimality between the locally optimal object in S and the globally optimal object in D . The optimality of a data object in turn is modeled by a utility function of the query user. Unlike traditional top- k queries, the k -regret query does not minimize the regret ratio for a specific utility function. Instead, it considers a family of infinite utility functions F , and aims to find a size- k subset that minimizes the maximum regret ratio of any utility function in F . Studies on k -regret queries have focused on the family of additive utility functions, which have limitations in modeling individuals’ preferences and decision-making processes, especially for a common observation called the diminishing marginal rate of substitution (DMRS). We introduce k -regret queries with multiplicative utility functions, which are more expressive in modeling the DMRS, to overcome those limitations. We propose a query algorithm with bounded regret ratios. To showcase the applicability of the algorithm, we apply it to a special family of multiplicative utility functions, the Cobb-Douglas family of utility functions, and a closely related family of utility functions, the Constant Elasticity of Substitution family of utility functions, both of which are frequently used utility functions in microeconomics. After a further study of the query properties, we propose a heuristic algorithm that produces even smaller regret ratios in practice. Extensive experiments on the proposed algorithms confirm that they consistently achieve small maximum regret ratios.

中文翻译：

---

使用乘法效用函数的 K-Regret 查询

这ķ-遗憾的查询旨在返回一个大小-ķ子集小号一个数据库的D这样，对于从该大小选择数据对象的任何查询用户-ķ子集小号而不是来自数据库D，她的遗憾率最小化。这里的遗憾率是通过局部最优对象之间最优性的相对差异来建模的小号和全局最优对象D. 反过来，数据对象的最优性由查询用户的效用函数建模。不同于传统的顶ķ查询，ķ-regret 查询不会最小化特定效用函数的遗憾率。相反，它考虑了一系列无限效用函数F，并旨在找到一个大小-ķ最小化任何效用函数的最大遗憾比的子集F. 研究ķ-regret 查询侧重于加性效用函数族，它们在建模个人偏好和决策过程方面存在局限性，特别是对于称为边际替代率递减 (DMRS) 的常见观察。我们介绍ķ- 具有乘法效用函数的遗憾查询，在 DMRS 建模中更具表现力，以克服这些限制。我们提出了一种具有有限遗憾率的查询算法。为了展示该算法的适用性，我们将其应用于特殊的乘法效用函数族，Cobb-Douglas 效用函数族，以及密切相关的效用函数族，效用函数的恒弹性替代族，两者是微观经济学中常用的效用函数。在进一步研究查询属性后，我们提出了一种启发式算法，该算法在实践中会产生更小的遗憾率。对所提出算法的广泛实验证实，它们始终能够实现小的最大遗憾率。