Probabilistic Preference Planning Problem for Markov Decision Processes

Abstract

The classical planning problem aims to find a sequence of permitted actions leading a system to a designed state, i.e., to achieve the system’s task. However, in many realistic cases we also have requirements on how to complete the task, indicating that some behaviors and situations are more preferred than others. In this paper, we present the probabilistic preference-based planning problem ( <inline-formula><tex-math notation="LaTeX">$\mathrm{P4}$</tex-math></inline-formula> ) for Markov decision processes, where the preferences are defined based on an enriched probabilistic LTL-style logic. We first recall <inline-formula><tex-math notation="LaTeX">$\mathrm{\mathrm{P4} {}Solver}$</tex-math></inline-formula> , an SMT-based planner computing the preferred plan by reducing the problem to a quadratic programming one previously developed to solve <inline-formula><tex-math notation="LaTeX">$\mathrm{P4}$</tex-math></inline-formula> . To improve computational efficiency and scalability, we then introduce a new encoding of the probabilistic preference-based planning problem as a multi-objective model checking one, and propose the corresponding planner <inline-formula><tex-math notation="LaTeX">$\mathrm{\mathrm{P4} {}Solver} _{{MO}}$</tex-math></inline-formula> . We illustrate the efficacy of both planners on some selected case studies to show that the model checking-based algorithm is considerably more efficient than the quadratic-programming-based one.