# Infinite horizon versus finite horizon MDP

1. When can we approximate a finite horizon MDP with infinite horizon?
2. Can we use infinite horizon stochastic shortest path problem on a directed acyclic graph?

Markov decision problem theory and computation is based on using backward induction (dynamic programming) to recursively evaluate expected rewards. When we define a policy $$\pi = (d_1, d_2,...,d_{N-1})$$, we assume that $$N$$, the length of horizon or the number of epochs is given.While in the infinite horizon the policies can be defined as, $$\nu = (d_1, d_2,...)$$ with no limitation on the length of the horizon.