k -regret queries with nonlinear utilities

In exploring representative databases, a primary issue has been finding accurate models of user preferences. Given this, our work generalizes the method of regret minimization as proposed by Nanongkai et al. to include nonlinear utility functions. Regret minimization is an approach for selecting k representative points from a database such that every user's ideal point in the entire database is similar to one of the k points. This approach combines benefits of the methods top- k and skyline; it controls the size of the output but does not require knowledge of users' preferences. Prior work with k -regret queries assumes users' preferences to be modeled by linear utility functions. In this paper, we derive upper and lower bounds for nonlinear utility functions, as these functions can better fit occurrences such as diminishing marginal returns, propensity for risk, and substitutability of preferences. To model these phenomena, we analyze a broad subset of convex, concave, and constant elasticity of substitution functions. We also run simulations on real and synthetic data to prove the efficacy of our bounds in practice.