K-Pleased Querying

Abstract

k-Regret Querying is a well studied problem to query a dataset <inline-formula><tex-math notation="LaTeX">$D$</tex-math></inline-formula> for a small subset <inline-formula><tex-math notation="LaTeX">$S$</tex-math></inline-formula> of size <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> with the minimal regret ratio for unknown utility functions. In this paper, we point out some issues in <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -Regret Querying, including the assumption of non-negative dataset and the lack of shift invariance. Known algorithms for <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -Regret Querying are limited in scope and result quality, and are based on the assumption of non-negative data. We introduce a new problem definition called <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -pleased querying for dealing with the shift variance issue, and propose a strategy of random sampling of the utility functions. This strategy is based on a study of the theoretical guarantee of the sampling approach. We also introduce a dimensionality reduction strategy, an improved greedy algorithm, and a study of other utility function sampling methods. All of our solutions can handle negative data. Theoretically, we derive a guarantee on the approximation attained by our sampling algorithm. Experimental results on numerous real datasets show that our proposed method is effective even with a small number of samples and small values of <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> .