从成对比较中学习用户对时序逻辑公式的偏好,构建可解释的决策模型。
Automata Learning of Preferences over Temporal Logic Formulas from Pairwise Comparisons
- 用带偏序关系的确定性有限自动机(PDFA)建模用户对时序目标的偏好
- 给出最小化PDFA的学习算法,在特征样本下可保证收敛
- 适用于机器人路径规划等需理解用户隐式偏好的场景
许多偏好获取算法针对命题逻辑公式或具有不同属性的项目。在序列决策中,用户的偏好可表现为对可能结果(每个为事件时序)的预序关系。本文研究一类偏好推断问题:用户的未知偏好以正则语言(时序序列集合)上的预序表示,称为时序目标。给定一组有限字词的成对比较,目标是同时学习时序目标集合及其间的预序。本文首先证明,时序目标上的偏好关系可用带偏序接受条件的偏好确定性有限自动机(PDFA)建模,偏好推断问题转化为学习PDFA。该问题计算复杂,判定是否存在小于给定整数 $k$ 的、与样本一致的PDFA是NP-完全的。本文形式化了特征样本的性质,并提出一个算法:在特征样本下,可保证学习到与真实PDFA等价的最小化PDFA。通过一个运行示例,并在机器人运动规划问题中进行详细分析验证方法有效性。
原文摘要 · Abstract (English)
Many preference elicitation algorithms consider preference over propositional logic formulas or items with different attributes. In sequential decision making, a user's preference can be a preorder over possible outcomes, each of which is a temporal sequence of events. This paper considers a class of preference inference problems where the user's unknown preference is represented by a preorder over regular languages (sets of temporal sequences), referred to as temporal goals. Given a finite set of pairwise comparisons between finite words, the objective is to learn both the set of temporal goals and the preorder over these goals. We first show that a preference relation over temporal goals can be modeled by a Preference Deterministic Finite Automaton (PDFA), which is a deterministic finite automaton augmented with a preorder over acceptance conditions. The problem of preference inference reduces to learning the PDFA. This problem is shown to be computationally challenging, with the problem of determining whether there exists a PDFA of size smaller than a given integer $k$, consistent with the sample, being NP-Complete. We formalize the properties of characteristic samples and develop an algorithm that guarantees to learn, given a characteristic sample, the minimal PDFA equivalent to the true PDFA from which the sample is drawn. We present the method through a running example and provide detailed analysis using a robotic motion planning problem.
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。