Hybrid Regret Minimization: A Submodular Approach (Extended Abstract)

In this paper, we investigate the hybrid regret min-imization (HRM) query, a new method to extract representative tuples from databases. The HRM query combines the two types of regret minimization queries in the literature, namely maximum regret minimization (MRM) and average regret minimization (ARM) queries, aiming to select a size-k subset of tuples from a database to simultaneously minimize the maximum and average regret ratios. We show the NP-hardness of the HRM problem and propose an asymptotic algorithmic (AA) framework with several optimization techniques and a multiplicative weights update (MWU) algorithm to process HRM queries efficiently with theoretical guarantees. Finally, we demonstrate that our proposed algorithms achieve better performance for HRM queries than existing methods specific to MRM and ARM queries through extensive experiments on real-world and synthetic datasets.