🤖 AI Summary
This work addresses the problem of inferring an unknown preference pre-order defined over regular languages—representing temporal objectives—from users’ pairwise comparisons of finite-length trajectory sequences. To formalize such preferences, we introduce Preference Deterministic Finite Automata (PDFAs), the first automaton model encoding temporal objective preferences via partial-order-labeled transitions on deterministic finite automata. Theoretically, we prove that learning a minimal PDFA is NP-complete and propose a provably correct learning algorithm based on characteristic samples, with polynomial query complexity. Experimentally, our method accurately recovers user preferences in realistic robot motion planning scenarios. This work establishes a foundational bridge between formal language theory and preference learning, delivering both theoretical guarantees and empirical validation for preference inference over structured temporal specifications.
📝 Abstract
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.