Singularly perturbed linear programs and Markov decision processes
  Linear programming formulations for the discounted and long-run average MDPs have evolved along separate trajectories. In 2006, E. Altman conjectured that the two linear programming formulations of discounted and long-run average MDPs are, most likely, a manifestation of general properties of singularly perturbed linear programs. In this note we demonstrate that this is, indeed, the case. 
Konstantin Avrachenkov (MAESTRO), Jerzy Filar, Vladimir Gaitsgory,   Andrew Stillman
math.OC