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<p>The double-factored Markov decision process (DFMDP) is a new framework for addressing the Markov decision processes with uncertainty of parameter scenarios.&#xa0;The two factors in this framework&#xa0;refer to the physical state and the scenario belief, which describes the probability distribution of scenarios, and they compose the state-belief pair&#xa0;for the framework. This study focuses on infinite horizon DFMDPs and their application. The optimality equations for infinite horizon DFMDPs are formulated and they can be represented by a value function mapping, which is a contraction under the supremum norm. It is demonstrated that for a fixed state, the optimal value functions for finite horizon DFMDPs are piecewise linear and convex in a scenario belief space. This property is used to develop an algorithm named as the double-factored linear support for an approximate solution to infinite horizon DFMDPs. The principle and framework of the algorithm are described in detail. Three computational instances are presented to illustrate the performance of the algorithm and the applications of infinite horizon DFMDPs.</p>

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Solution for Infinite Horizon Double-Factored Markov Decision Processes with Application

  • 期刊论文

  • 发表日期：

    2025年10月2日

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  • Chengjun Hou

摘要

The double-factored Markov decision process (DFMDP) is a new framework for addressing the Markov decision processes with uncertainty of parameter scenarios. The two factors in this framework refer to the physical state and the scenario belief, which describes the probability distribution of scenarios, and they compose the state-belief pair for the framework. This study focuses on infinite horizon DFMDPs and their application. The optimality equations for infinite horizon DFMDPs are formulated and they can be represented by a value function mapping, which is a contraction under the supremum norm. It is demonstrated that for a fixed state, the optimal value functions for finite horizon DFMDPs are piecewise linear and convex in a scenario belief space. This property is used to develop an algorithm named as the double-factored linear support for an approximate solution to infinite horizon DFMDPs. The principle and framework of the algorithm are described in detail. Three computational instances are presented to illustrate the performance of the algorithm and the applications of infinite horizon DFMDPs.