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.

使用局部有序偏好对具有时限目标的马尔可夫决策过程进行决策和概率规划，将部分有序偏好通过引入顺序理论映射到这些目标的偏好决策，从而综合出最喜欢的策略。

偏好基于规划的随机环境：从部分有序时态目标到最受欢迎的策略

Preference-Based Planning in Stochastic Environments: From  Partially-Ordered Temporal Goals to Most Preferred Policies

Goal Recognition is the task of discerning the correct intended goal that an
agent aims to achieve, given a set of goal hypotheses, a domain model, and a
sequence of observations (i.e., a sample of the plan executed in the
environment). Existing approaches assume that goal hypotheses comprise a single
conjunctive formula over a single final state and that the environment dynamics
are deterministic, preventing the recognition of temporally extended goals in
more complex settings. In this paper, we expand goal recognition to temporally
extended goals in Fully Observable Non-Deterministic (FOND) planning domain
models, focusing on goals on finite traces expressed in Linear Temporal Logic
(LTLf) and Pure Past Linear Temporal Logic (PLTLf). We develop the first
approach capable of recognizing goals in such settings and evaluate it using
different LTLf and PLTLf goals over six FOND planning domain models. Empirical
results show that our approach is accurate in recognizing temporally extended
goals in different recognition settings.

本文研究将目标识别扩展到具有完整可观察性和非确定性的计划领域模型中，重点是在使用线性时间逻辑（LTLf）和纯过去线性时间逻辑（PLTLf）表达的有限痕迹上识别目标。我们开发了第一种能够识别此类设置中目标的方法，并使用六个计划领域模型上的不同 LTLf 和 PLTLf 目标进行评估，实验结果表明我们的方法在不同的识别设置中识别时间上延长的目标是准确的。