3 research outputs found
Extreme occupation measures in Markov decision processes with a cemetery
In this paper, we consider a Markov decision process (MDP) with a Borel state
space , where is an absorbing state
(cemetery), and a Borel action space . We consider the space of
finite occupation measures restricted on , and the
extreme points in it. It is possible that some strategies have infinite
occupation measures. Nevertheless, we prove that every finite extreme
occupation measure is generated by a deterministic stationary strategy. Then,
for this MDP, we consider a constrained problem with total undiscounted
criteria and constraints, where the cost functions are nonnegative. By
assumption, the strategies inducing infinite occupation measures are not
optimal. Then, our second main result is that, under mild conditions, the
solution to this constrained MDP is given by a mixture of no more than
occupation measures generated by deterministic stationary strategies