This paper presents an efficient preference elicitation framework for uncertain matroid optimization, where precise weight information is unavailable, but insights into possible weight values are accessible. The core innovation of our approach lies in its ability to systematically elicit user preferences, aligning the optimization process more closely with decision-makers' objectives. By incrementally querying preferences between pairs of elements, we iteratively refine the parametric uncertainty regions, leveraging the structural properties of matroids. Our method aims to achieve the exact optimum by reducing regret with a few elicitation rounds. Additionally, our approach avoids the computation of Minimax Regret and the use of Linear programming solvers at every iteration, unlike previous methods. Experimental results on four standard matroids demonstrate that our method reaches optimality more quickly and with fewer preference queries than existing techniques.

翻译：本文提出了一种针对不确定性拟阵优化的高效偏好启发框架，该框架适用于权重信息不精确但可能权重值范围可获取的场景。本方法的核心创新在于能够系统性地启发用户偏好，使优化过程更紧密地贴合决策者的目标。通过逐步查询元素对之间的偏好关系，我们利用拟阵的结构特性迭代优化参数不确定性区域。该方法旨在通过少量启发轮次降低遗憾值，从而获得精确最优解。与先前方法不同，本方法在每次迭代中避免了极小极大遗憾值的计算及线性规划求解器的使用。在四种标准拟阵上的实验结果表明，相较于现有技术，本方法能以更少的偏好查询次数更快地达到最优状态。