K-Regret Queries Using Multiplicative Utility Functions

Abstract

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.