Finding Average Regret Ratio Minimizing Set in Database

Abstract

Selecting a certain number of data points (or records) from a database which "best" satisfy users' expectations is a very prevalent problem with many applications. One application is a hotel booking website showing a certain number of hotels on a single page. However, this problem is very challenging since the selected points should "collectively" satisfy the expectation of all users. Showing a certain number of data points to a single user could decrease the satisfaction of a user because the user may not be able to see his/her favorite point which could be found in the original database. In this paper, we would like to find a set of k points such that on average, the satisfaction (ratio) of a user is maximized. This problem takes into account the probability distribution of the users and considers the satisfaction (ratio) of all users, which is more reasonable in practice, compared with the existing studies that only consider the worst-case satisfaction (ratio) of the users, which may not reflect the whole population and is not useful in some applications. Motivated by this, in this paper, we propose algorithms for this problem. Finally, we conducted experiments to show the effectiveness and the efficiency of the algorithms.Definition 5 (Variance of Regret Ratio). Let F be a set of users with the probability density function η(.) and S be a subset of D. The variance of regret ratio of F for S, denoted by vrr(S), is defined to be f ∈F (rr(S, f ) − arr(S)) 2 η(f )df .Although the FAM problem focuses on minimizing average regret ratio, it is important for a set S to have low vrr(S) as well. In our empirical studies (Section V), we use estimates of vrr(S) to compare different selection sets.

Efficient processing of k-regret minimization queries with theoretical guarantees

“…Faulkner et al [5] and Qi et al [7] extended the linear utility functions to CONVEX, CONCAVE, CES utility functions and multiplicative utility functions for k-regret queries. Zeighami and Wong [35] proposed the metric of the average regret ratio to measure user satisfaction. To reduce the bounds of the regret ratio, Nanongkai et al [23] and Xie et al [36] combined user interactions into the process of selection.…”

“…Moreover, Xie et al [36] provide a strongly truthful interactive mechanism to leverage the regret ratios using true database tuples instead of artificial ones and provide provable performance guarantees. Zeighami and Wong [39] propose the metric of average regret ratio to measure user's satisfaction and further develop efficient algorithms to solve it [35]. Also, based on regret minimization concepts, [13], [37] focus on the compact maxima and rank regret representative problems, respectively.…”

A Fully Dynamic Algorithm for k-Regret Minimizing Sets

“…The difference between RRR and RMS is that the regret in RRR is defined by ranking while the regret in RMS is defined by score. Several studies [14], [34], [35] investigated the average regret minimization (ARM) problem. Instead of minimizing the maximum regret ratio, ARM returns a subset of r tuples such that the average regret of all possible users is minimized.…”

A Fully Dynamic Algorithm for k-Regret Minimizing Sets

“…The difference between RRR and RMS is that the regret in RRR is defined by ranking while the regret in RMS is defined by score. Several studies [26], [28], [35] investigated the average regret minimization (ARM) problem. Instead of minimizing the maximum regret ratio, ARM returns a subset of r tuples such that the average regret of all possible users is minimized.…”