Determining the Optimal Strategies for Antagonistic Positional Games in Markov Decision Processes

2012 ◽  
pp. 229-234
Author(s):  
Dmitrii Lozovanu ◽  
Stefan Pickl
Keyword(s):  
Markov Decision Processes ◽  
Optimal Strategies ◽  
Decision Processes ◽  
Positional Games ◽  
Markov Decision

scholarly journals Exact Decomposition Approaches for Markov Decision Processes: A Survey

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Cherki Daoui ◽  
Mohamed Abbad ◽  
Mohamed Tkiouat
Keyword(s):  
Markov Decision Processes ◽  
Optimal Strategies ◽  
Decision Processes ◽  
Divide And Conquer ◽  
The Past ◽  
Large State Space ◽  
Aggregation Techniques ◽  
Markov Decision ◽  
Pros And Cons ◽  
Special Case

As classical methods are intractable for solving Markov decision processes (MDPs) requiring a large state space, decomposition and aggregation techniques are very useful to cope with large problems. These techniques are in general a special case of the classic Divide-and-Conquer framework to split a large, unwieldy problem into smaller components and solving the parts in order to construct the global solution. This paper reviews most of decomposition approaches encountered in the associated literature over the past two decades, weighing their pros and cons. We consider several categories of MDPs (average, discounted, and weighted MDPs), and we present briefly a variety of methodologies to find or approximate optimal strategies.

Markov Decision Processes and Determining Nash Equilibria for Stochastic Positional Games

2011 ◽  
Vol 44 (1) ◽  
pp. 13398-13403 ◽  
Author(s):  
Dmitrii Lozovanu ◽  
Stefan Pickl ◽  
Erik Kropat
Keyword(s):  
Markov Decision Processes ◽  
Nash Equilibria ◽  
Decision Processes ◽  
Positional Games ◽  
Markov Decision

On a reduction principle in dynamic programming

1988 ◽  
Vol 20 (04) ◽  
pp. 836-851
Author(s):  
K. D. Glazebrook
Keyword(s):  
Dynamic Programming ◽  
Markov Decision Processes ◽  
Sufficient Conditions ◽  
Optimal Strategies ◽  
Decision Processes ◽  
Reduction Principle ◽  
The Status ◽  
Markov Decision ◽  
The Individual ◽  
Necessary And Sufficient

Whittle enunciated an important reduction principle in dynamic programming when he showed that under certain conditions optimal strategies for Markov decision processes (MDPs) placed in parallel to one another take actions in a way which is consistent with the optimal strategies for the individual MDPs. However, the necessary and sufficient conditions given by Whittle are by no means always satisfied. We explore the status of this computationally attractive reduction principle when these conditions fail.

On a reduction principle in dynamic programming

1988 ◽  
Vol 20 (4) ◽  
pp. 836-851 ◽  
Author(s):  
K. D. Glazebrook
Keyword(s):  
Dynamic Programming ◽  
Markov Decision Processes ◽  
Sufficient Conditions ◽  
Optimal Strategies ◽  
Decision Processes ◽  
Reduction Principle ◽  
The Status ◽  
Markov Decision ◽  
The Individual ◽  
Necessary And Sufficient

Whittle enunciated an important reduction principle in dynamic programming when he showed that under certain conditions optimal strategies for Markov decision processes (MDPs) placed in parallel to one another take actions in a way which is consistent with the optimal strategies for the individual MDPs. However, the necessary and sufficient conditions given by Whittle are by no means always satisfied. We explore the status of this computationally attractive reduction principle when these conditions fail.

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