Sarah H.Q. Li , Assalé Adjé , Pierre-Loïc Garoche , Behçet Açıkmeşe
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Set-based value operators for non-stationary and uncertain Markov decision processes
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.
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.