Optimal and Nearly Optimal Policies in Markov Decision Chains with Nonnegative Rewards and Risk-Sensitive Expected Total-Reward Criterion

2002 ◽  
pp. 189-221
Author(s):  
Rolando Cavazos-Cadena ◽  
Raúl Montes-de-Oca
Keyword(s):  
Total Reward ◽  
Risk Sensitive ◽  
Optimal Policies ◽  
Markov Decision ◽  
Reward Criterion

On theory and algorithms for Markov decision problems with the total reward criterion

OR Spectrum ◽  
1979 ◽  
Vol 1 (1) ◽  
pp. 57-67 ◽  
Author(s):  
J. A. E. E. van Nunen ◽  
J. Wessels
Keyword(s):  
Decision Problems ◽  
Total Reward ◽  
Markov Decision Problems ◽  
Markov Decision ◽  
Reward Criterion

scholarly journals Optimal Policies for Quantum Markov Decision Processes

2021 ◽  
Author(s):  
Ming-Sheng Ying ◽  
Yuan Feng ◽  
Sheng-Gang Ying
Keyword(s):  
Decision Making ◽  
Reinforcement Learning ◽  
Quantum Systems ◽  
Sequential Decision Making ◽  
Mathematical Framework ◽  
Sequential Decision ◽  
Learning Techniques ◽  
Optimal Policies ◽  
Markov Decision ◽  
Programming Algorithms

AbstractMarkov decision process (MDP) offers a general framework for modelling sequential decision making where outcomes are random. In particular, it serves as a mathematical framework for reinforcement learning. This paper introduces an extension of MDP, namely quantum MDP (qMDP), that can serve as a mathematical model of decision making about quantum systems. We develop dynamic programming algorithms for policy evaluation and finding optimal policies for qMDPs in the case of finite-horizon. The results obtained in this paper provide some useful mathematical tools for reinforcement learning techniques applied to the quantum world.

Optimal stationary strategies in leavable Markov decision processes

1990 ◽  
Vol 27 (01) ◽  
pp. 134-145
Author(s):  
Matthias Fassbender
Keyword(s):  
Transition Probabilities ◽  
Practical Applications ◽  
Stationary Strategies ◽  
Countable State ◽  
Markov Decision ◽  
Bias Optimality ◽  
The Mean ◽  
Optimal Stationary Strategies ◽  
The Cost ◽  
Reward Criterion

This paper establishes the existence of an optimal stationary strategy in a leavable Markov decision process with countable state space and undiscounted total reward criterion. Besides assumptions of boundedness and continuity, an assumption is imposed on the model which demands the continuity of the mean recurrence times on a subset of the stationary strategies, the so-called ‘good strategies'. For practical applications it is important that this assumption is implied by an assumption about the cost structure and the transition probabilities. In the last part we point out that our results in general cannot be deduced from related works on bias-optimality by Dekker and Hordijk, Wijngaard or Mann.

Nash equilibria in a class of Markov stopping games with total reward criterion

2021 ◽  
Author(s):  
Rolando Cavazos-Cadena ◽  
Mario Cantú-Sifuentes ◽  
Imelda Cerda-Delgado
Keyword(s):  
Nash Equilibria ◽  
Total Reward ◽  
Stopping Games ◽  
Reward Criterion
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