We study the problem of learning near-optimal behavior in finite Markov Decision Processes (MDPs) with a polynomial number of samples. These “PAC-MDP” algorithms include the wellknown E3 and R-MAX algorithms as well as the more recent Delayed Q-learning algorithm. We summarize the current state-of-the-art by presenting bounds for the problem in a unified theoretical framework. A more refined analysis for upper and lower bounds is presented to yield insight into the differences between the model-free Delayed Q-learning and the model-based R-MAX.