Improved Algorithm for Regret Ratio Minimization in Multi-Objective Submodular Maximization

Submodular maximization has attracted extensive attention due to its numerous applications in machine learning and artificial intelligence. Many real-world problems require maximizing multiple submodular objective functions at the same time. In such cases, a common approach is select representative subset of Pareto optimal solutions with different trade-offs among objectives. To this end, paper, we investigate regret ratio minimization (RRM) problem multi-objective maximization, which aims find most k best approximate all w.r.t. any linear combination functions. We propose novel HS-RRM algorithm by transforming RRM into HittingSet based on notions ε-kernel δ-net, where α-approximation for single-objective used as an oracle. improve upon previous best-known bound maximum (MRR) output show that new nearly asymptotically fixed number d Experiments synthetic data confirm achieves lower MRRs than existing algorithms.