加权信号时序逻辑公式在排序学习中的表达能力
Expressive Power of WSTL Formulas for Learning to Rank
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中文总结 AI 辅助
本研究从理论上验证WSTL公式作为排序学习评分函数的表达能力，提出秩可实现性与秩容量的概念，并通过混合整数线性规划及实验证明其有效性。
中文摘要 AI 辅助
加权信号时序逻辑（WSTL）越来越多地被用作具有安全保证的轨迹排序学习问题中的评分函数，其加权定量语义充当参数化的效用函数。尽管兴趣日益增长，先前的工作仅假设WSTL公式的表达能力，并通过经验证明其在捕获多样化偏好方面的实用性。本研究关注这一假设的正确性，并探讨使用WSTL公式作为评分函数是否具有理论依据。我们形式化了两个概念：第一，秩可实现性，即通过改变权重是否可以实现给定信号集的所有排序；第二，秩容量，即公式可实现秩的最大信号集大小。我们提出一个混合整数线性规划来判断秩可实现性，并推导出秩容量的构造性下界。在机器人导航任务上的实验表明，虽然一个实际的WSTL规范在具有相似轨迹的集合上可能无法实现秩，但其秩容量超过了轨迹集的大小。对布尔等价公式的分析表明，公式结构影响表达能力，并且可以在不改变定性语义的情况下增加秩容量。
英文摘要
Weighted Signal Temporal Logic (WSTL) is increasingly used as a scoring function in learning-to-rank problems of trajectories with safety guarantees, where its weighted quantitative semantics serve as a parametrized utility function. Despite the growing interest, prior work only assumes the expressiveness of WSTL formulas and empirically demonstrates its utility in capturing diverse preferences. This work focuses on the correctness of this assumption and asks whether using WSTL formulas as scoring functions is theoretically justified. We formalize two concepts: first, rank-realizability, which asks whether all rankings of a given signal set are achievable by varying weights, and, second, rank-capacity, the maximum signal set size for which the formula is rank-realizable. We propose a Mixed-Integer Linear Program to decide rank-realizability, and derive constructive lower bounds for rank-capacity. Experiments on a robotic navigation task show that while a practical WSTL specification may fail to be rank-realizable on a set with similar trajectories, its rank-capacity exceeds the size of the trajectory set. Analysis of Boolean-equivalent formulas reveals that formula structure affects expressivity and that rank-capacity can be increased without altering qualitative semantics.
发表机构
- University of Michigan（密歇根大学）
- Lehigh University（利哈伊大学）
- Virginia Commonwealth University（弗吉尼亚联邦大学）
机构由 AI 辅助整理，请以论文原文为准。
