Pareto Optimization with Robust Evaluation for Noisy Subset Selection

Abstract

Subset selection is a fundamental problem in combinatorial optimization, which has a wide range of applications such as influence maximization and sparse regression. The goal is to select a subset of limited size from a ground set in order to maximize a given objective function. However, the evaluation of the objective function in real-world scenarios is often noisy. Previous algorithms, including the greedy algorithm and multi-objective evolutionary algorithms POSS and PONSS, either struggle in noisy environments or consume excessive computational resources. In this paper, we focus on the noisy subset selection problem with a cardinality constraint, where the evaluation of a subset is noisy. We propose a novel approach based on Pareto Optimization with Robust Evaluation for noisy subset selection (PORE), which maximizes a robust evaluation function and minimizes the subset size simultaneously. PORE can efficiently identify well-structured solutions and handle computational resources, addressing the limitations observed in PONSS. Our experiments, conducted on real-world datasets for influence maximization and sparse regression, demonstrate that PORE significantly outperforms previous methods, including the classical greedy algorithm, POSS, and PONSS. Further validation through ablation studies confirms the effectiveness of our robust evaluation function.