Set-based value operators for non-stationary and uncertain Markov decision processes

IF 4.8 2区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Automatica Pub Date : 2024-10-28 DOI:10.1016/j.automatica.2024.111970
Sarah H.Q. Li , Assalé Adjé , Pierre-Loïc Garoche , Behçet Açıkmeşe
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Abstract

This paper analyzes finite-state Markov Decision Processes (MDPs) with nonstationary and uncertain parameters via set-based fixed point theory. Given compact parameter ambiguity sets, we demonstrate that a family of contraction operators, including the Bellman operator and the policy evaluation operator, can be extended to set-based contraction operators with a unique fixed point—a compact value function set. For non-stationary MDPs, we show that while the value function trajectory diverges, its Hausdorff distance from this fixed point converges to zero. In parameter uncertain MDPs, the fixed point’s extremum value functions are equivalent to the min–max value function in robust dynamic programming under the rectangularity condition. Furthermore, we show that the rectangularity condition is a sufficient condition for the fixed point to contain its own extremum value functions. Finally, we derive novel guarantees for probabilistic path planning in capricious wind fields and stratospheric station-keeping.
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非稳态和不确定马尔可夫决策过程的基于集合的值算子
本文通过基于集合的定点理论分析了具有非稳态和不确定参数的有限状态马尔可夫决策过程(MDP)。给定紧凑的参数模糊集,我们证明包括贝尔曼算子和策略评估算子在内的一系列收缩算子可以扩展为具有唯一固定点--紧凑的价值函数集--的基于集合的收缩算子。对于非稳态 MDP,我们证明了虽然价值函数轨迹会发散,但其与该固定点的豪斯多夫距离会收敛为零。在参数不确定的 MDPs 中,在矩形条件下,固定点的极值函数等同于鲁棒动态程序设计中的最小值函数。此外,我们还证明了矩形条件是定点包含自身极值函数的充分条件。最后,我们推导出了在反复无常的风场和平流层定站中进行概率路径规划的新保证。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Automatica
Automatica 工程技术-工程:电子与电气
CiteScore
10.70
自引率
7.80%
发文量
617
审稿时长
5 months
期刊介绍: Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.
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