Smooth Value and Policy Functions for Discounted Dynamic Programming

We consider a discounted dynamic program in which the spaces of states and actions are smooth (in a sense that is suitable for the problem at hand) manifolds. We give conditions that insure that the optimal policy and the value function are smooth functions of the state when the discount factor is small. In addition, these functions vary in a Lipschitz manner as the reward function-discount factor pair varies in a neighborhood of the pair consisting of a given reward function and zero. Running Title: Smooth Value and Policy Functions