WFAs are non-deterministic and so not immediately analogous to RNNs.

Neural Information Processing Systems http://nips.cc/

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.

This work studies the question of learning probabilistic deterministic automata from language models. For this purpose, it focuses on analyzing the relations defined on algebraic structures over strings by equivalences and similarities on probability distributions. We introduce a congruence that extends the classical Myhill-Nerode congruence for formal languages. This new congruence is the basis for defining regularity over language models. We present an active learning algorithm that computes the quotient with respect to this congruence whenever the language model is regular. The paper also defines the notion of recognizability for language models and shows that it coincides with regularity for congruences. For relations which are not congruences, it shows that this is not the case. Finally, it discusses the impact of this result on learning in the context of language models.

Specifying tasks for robotic systems traditionally requires coding expertise, deep domain knowledge, and significant time investment. While learning from demonstration offers a promising alternative, existing methods often struggle with tasks of longer horizons. To address this limitation, we introduce a computationally efficient approach for learning probabilistic deterministic finite automata (PDFA) that capture task structures and expert preferences directly from demonstrations. Our approach infers sub-goals and their temporal dependencies, producing an interpretable task specification that domain experts can easily understand and adjust. We validate our method through experiments involving object manipulation tasks, showcasing how our method enables a robot arm to effectively replicate diverse expert strategies while adapting to changing conditions.

We define a congruence that copes with null next-symbol probabilities that arise when the output of a language model is constrained by some means during text generation. We develop an algorithm for efficiently learning the quotient with respect to this congruence and evaluate it on case studies for analyzing statistical properties of LLM.

Human preferences are not always represented via complete linear orders: It is natural to employ partially-ordered preferences for expressing incomparable outcomes. In this work, we consider decision-making and probabilistic planning in stochastic systems modeled as Markov decision processes (MDPs), given a partially ordered preference over a set of temporally extended goals. Specifically, each temporally extended goal is expressed using a formula in Linear Temporal Logic on Finite Traces (LTL$_f$). To plan with the partially ordered preference, we introduce order theory to map a preference over temporal goals to a preference over policies for the MDP. Accordingly, a most preferred policy under a stochastic ordering induces a stochastic nondominated probability distribution over the finite paths in the MDP. To synthesize a most preferred policy, our technical approach includes two key steps. In the first step, we develop a procedure to transform a partially ordered preference over temporal goals into a computational model, called preference automaton, which is a semi-automaton with a partial order over acceptance conditions. In the second step, we prove that finding a most preferred policy is equivalent to computing a Pareto-optimal policy in a multi-objective MDP that is constructed from the original MDP, the preference automaton, and the chosen stochastic ordering relation. Throughout the paper, we employ running examples to illustrate the proposed preference specification and solution approaches. We demonstrate the efficacy of our algorithm using these examples, providing detailed analysis, and then discuss several potential future directions.

We present the efficient implementations of probabilistic deterministic finite automaton learning methods available in FlexFringe. These implement well-known strategies for state-merging including several modifications to improve their performance in practice. We show experimentally that these algorithms obtain competitive results and significant improvements over a default implementation. We also demonstrate how to use FlexFringe to learn interpretable models from software logs and use these for anomaly detection. Although less interpretable, we show that learning smaller more convoluted models improves the performance of FlexFringe on anomaly detection, outperforming an existing solution based on neural nets.

We propose a novel Bayesian nonparametric approach to learning with probabilistic deterministic finite automata (PDFA). We define and develop and sampler for a PDFA with an infinite number of states which we call the probabilistic deterministic infinite automata (PDIA). Posterior predictive inference in this model, given a finite training sequence, can be interpreted as averaging over multiple PDFAs of varying structure, where each PDFA is biased towards having few states. We suggest that our method for averaging over PDFAs is a novel approach to predictive distribution smoothing. We test PDIA inference both on PDFA structure learning and on both natural language and DNA data prediction tasks.

In this paper, we study planning in stochastic systems, modeled as Markov decision processes (MDPs), with preferences over temporally extended goals. Prior work on temporal planning with preferences assumes that the user preferences form a total order, meaning that every pair of outcomes are comparable with each other. In this work, we consider the case where the preferences over possible outcomes are a partial order rather than a total order. We first introduce a variant of deterministic finite automaton, referred to as a preference DFA, for specifying the user's preferences over temporally extended goals. Based on the order theory, we translate the preference DFA to a preference relation over policies for probabilistic planning in a labeled MDP. In this treatment, a most preferred policy induces a weak-stochastic nondominated probability distribution over the finite paths in the MDP. The proposed planning algorithm hinges on the construction of a multi-objective MDP. We prove that a weak-stochastic nondominated policy given the preference specification is Pareto-optimal in the constructed multi-objective MDP, and vice versa. Throughout the paper, we employ a running example to demonstrate the proposed preference specification and solution approaches. We show the efficacy of our algorithm using the example with detailed analysis, and then discuss possible future directions.