用单调效用函数高效选出符合偏好的多目标优化解。
Modeling Multi-Objective Tradeoffs with Monotonic Utility Functions
- 先密集采样用户关注区域，再稀疏化为少量代表性解。
- 5个点就能保留99%以上整体效用，比现有方法高3%以上。
- 适合医疗、工程、大模型等需要快速决策的场景。
多目标优化中，决策者需从帕累托最优解集中选择符合偏好的解。由于评估成本高且权衡空间维度大，全面探索帕累托前沿不可行。本文提出一种两步法：首先在用户关注区域密集采样帕累托前沿，然后将其稀疏化为一个小型、多样化的解集。我们以软硬约束函数（SHFs）为例，该类函数可直观实现专家常用的软硬边界策略。在多种场景（包括近距离放射治疗、工程设计和大语言模型）中进行了充分验证。对于近距离放射治疗，本方法返回的紧凑解集在SHF定义下的效用高于次优方法超3%；在其他领域，仅5个点即可捕获原始密集解集99%以上的效用。
原文摘要 · Abstract (English)
Countless science and engineering applications in multi-objective optimization (MOO) necessitate that decision-makers (DMs) select a Pareto-optimal (PO) solution which aligns with their preferences. Evaluating individual solutions is often expensive, and the high-dimensional trade-off space makes exhaustive exploration of the full Pareto frontier (PF) infeasible. We introduce a novel, principled two-step process for obtaining a compact set of PO points that aligns with user preferences, which are specified a priori as general monotonic utility functions (MFs). Our process (1) densely samples the user's region of interest on the PF, then (2) sparsifies the results into a small, diverse set for the DM. We instantiate this framework with soft-hard functions (SHFs), an intuitive class of MFs that operationalizes the common expert heuristic of imposing soft and hard bounds. We provide extensive empirical validation of our framework instantiated with SHFs on diverse domains, including brachytherapy, engineering design, and large language models. For brachytherapy, our approach returns a compact set of points with over 3% greater SHF-defined utility than the next best approach. Among the other domains, our approach consistently leads in utility, as a final compact set of just 5 points captures over 99% of the utility offered by the entire dense set.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。