Value iteration for approximate dynamic programming under convexity

Abstract

This paper studies value iteration for infinite horizon contracting Markov decision processes under convexity assumptions and when the state space is uncountable. The original value iteration is replaced with a more tractable form and the fixed points from the modified Bellman operators will be shown to converge uniformly on compacts sets to their original counterparts. This holds under various sampling approaches for the random disturbances. Moreover, this paper will present conditions in which these fixed points form monotone sequences of lower bounding or upper bounding functions for the original fixed point. This approach is then demonstrated numerically on a perpetual Bermudan put option.