
From:  Philippe Preux 
Subject:  [Helpglpk] existence of the solution for the LP formulation of Markov decision problem 
Date:  Thu, 24 Apr 2008 15:21:57 +0200 
Useragent:  MozillaThunderbird 2.0.0.6 (X11/20071009) 
Hi,I am interesting in Markov decision problems, let's say in the discrete setting, infinite horizon with accumulated discounted reward. I assume rewards are bounded. In this case, we know from the theory of MDPs that the value function always exists.
The formulation of this problem as an LP problem is wellknown.We know from MDP theory that, since the value function exists, is unique, and is bounded, and the optimal policy exists too, that the primal and dual of the equivalent LP formulation are bounded feasible. Now, my question is: let us suppose we only have the problem under its LP guise and we do not know it is bounded feasible; would there be a way to know by simply looking at it (not trying to solve it), I mean, just knowing A and b, that this problem is bounded, feasible in the primal and the dual?
Thanks for any hint Philippe
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