scholarly journals Sample-Path Optimal Stationary Policies in Stable Markov Decision Chains with the Average Reward Criterion

2015 ◽  
Vol 52 (2) ◽  
pp. 419-440
Author(s):  
Rolando Cavazos-Cadena ◽  
Raúl Montes-De-Oca ◽  
Karel Sladký
Keyword(s):  
Sample Path ◽  
Point Of View ◽  
Average Reward ◽  
Stationary Policy ◽  
Optimality Equation ◽  
Markov Decision ◽  
Average Reward Criterion ◽  
Compact Action Sets ◽  
Path Point ◽  
Reward Criterion

This paper concerns discrete-time Markov decision chains with denumerable state and compact action sets. Besides standard continuity requirements, the main assumption on the model is that it admits a Lyapunov function ℓ. In this context the average reward criterion is analyzed from the sample-path point of view. The main conclusion is that if the expected average reward associated to ℓ2 is finite under any policy then a stationary policy obtained from the optimality equation in the standard way is sample-path average optimal in a strong sense.

Sample-Path Optimal Stationary Policies in Stable Markov Decision Chains with the Average Reward Criterion

2015 ◽  
Vol 52 (02) ◽  
pp. 419-440 ◽  
Author(s):  
Rolando Cavazos-Cadena ◽  
Raúl Montes-De-Oca ◽  
Karel Sladký
Keyword(s):  
Sample Path ◽  
Point Of View ◽  
Average Reward ◽  
Stationary Policy ◽  
Optimality Equation ◽  
Markov Decision ◽  
Average Reward Criterion ◽  
Compact Action Sets ◽  
Path Point ◽  
Reward Criterion

This paper concerns discrete-time Markov decision chains with denumerable state and compact action sets. Besides standard continuity requirements, the main assumption on the model is that it admits a Lyapunov function ℓ. In this context the average reward criterion is analyzed from the sample-path point of view. The main conclusion is that if the expected average reward associated to ℓ2is finite under any policy then a stationary policy obtained from the optimality equation in the standard way is sample-path average optimal in a strong sense.

Semi-Markov decision processes with polynomial reward

1982 ◽  
Vol 19 (2) ◽  
pp. 301-309 ◽  
Author(s):  
Zvi Rosberg
Keyword(s):  
Transition Period ◽  
Queueing Network ◽  
Decision Processes ◽  
Average Reward ◽  
Network Scheduling ◽  
Long Run ◽  
Markov Decision ◽  
Average Reward Criterion ◽  
Long Run Average Reward ◽  
Reward Criterion

A semi-Markov decision process, with a denumerable multidimensional state space, is considered. At any given state only a finite number of actions can be taken to control the process. The immediate reward earned in one transition period is merely assumed to be bounded by a polynomial and a bound is imposed on a weighted moment of the next state reached in one transition. It is shown that under an ergodicity assumption there is a stationary optimal policy for the long-run average reward criterion. A queueing network scheduling problem, for which previous criteria are inapplicable, is given as an application.

VECTOR-VALUED MARKOV DECISION PROCESSES WITH AVERAGE REWARD CRITERION: THE MULTICHAIN CASE

2000 ◽  
Vol 14 (4) ◽  
pp. 533-548
Author(s):  
Kazuyoshi Wakuta
Keyword(s):  
Decision Process ◽  
Decision Processes ◽  
Iteration Algorithm ◽  
Average Reward ◽  
Markov Decision ◽  
Policy Iteration Algorithm ◽  
Average Reward Criterion ◽  
Systems Of Linear Inequalities ◽  
Vector Valued ◽  
Reward Criterion

We study the multichain case of a vector-valued Markov decision process with average reward criterion. We characterize optimal deterministic stationary policies via systems of linear inequalities and discuss a policy iteration algorithm for finding all optimal deterministic stationary policies.

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