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.

翻译：子集选择是组合优化中的一个基本问题，在影响力最大化和稀疏回归等领域具有广泛应用。其目标是从候选集中选出有限大小的子集以最大化给定目标函数。然而，现实场景中的目标函数评估通常存在噪声。现有算法，包括贪心算法和多目标进化算法POSS与PONSS，要么难以应对噪声环境，要么消耗过多计算资源。本文聚焦于含噪声评估的基数约束子集选择问题，提出一种基于鲁棒评估的帕累托优化新方法（PORE），该方法同时最大化鲁棒评估函数并最小化子集规模。PORE能够高效识别结构优良的解并合理管理计算资源，有效克服了PONSS的局限性。我们在影响力最大化和稀疏回归的真实数据集上进行的实验表明，PORE显著优于包括经典贪心算法、POSS和PONSS在内的现有方法。消融研究进一步验证了所提出鲁棒评估函数的有效性。