A linear programming based approach for composite-action Markov decision processes
RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 5, pp. 1749-1761.

We study a time homogeneous discrete composite-action Markov decision process (CMDP) which needs to make multiple decisions at each state. In this particular Markov decision process, the state variables are divided into two separable sets and a two-dimensional composite action is chosen at each decision epoch. To solve a composite-action Markov decision process, we propose a novel linear programming model (Contracted Linear Programming Model, CLPM). We show that the CLPM model obtains the optimal state values of a CMDP process. We analyze and compare the number of variables and constraints of the CLPM model and the Traditional Linear Programming Model (TLPM). Computational experiments compare running times and memory usage of the two models. The CLPM model outperforms the TLPM model in both time complexity and space complexity by theoretical analysis and computational experiments.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2018081
Classification : 90C40, 90C05
Mots-clés : Markov decision process, linear programming, optimal state value, action
Zhang, Zhicong 1 ; Li, Shuai 1 ; Yan, Xiaohui 1 ; Zhang, Liangwei 1

1 
@article{RO_2019__53_5_1749_0,
     author = {Zhang, Zhicong and Li, Shuai and Yan, Xiaohui and Zhang, Liangwei},
     title = {A linear programming based approach for composite-action {Markov} decision processes},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {1749--1761},
     publisher = {EDP-Sciences},
     volume = {53},
     number = {5},
     year = {2019},
     doi = {10.1051/ro/2018081},
     mrnumber = {4016528},
     zbl = {1431.90173},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ro/2018081/}
}
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Zhang, Zhicong; Li, Shuai; Yan, Xiaohui; Zhang, Liangwei. A linear programming based approach for composite-action Markov decision processes. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 5, pp. 1749-1761. doi : 10.1051/ro/2018081. http://archive.numdam.org/articles/10.1051/ro/2018081/

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