We consider the most realistic reinforcement learning setting in which an agent starts in an unknown environment (the POMDP) and must follow one continuous and uninterrupted chain of experience with no access to "resets" or "offline" simulation. We provide algorithms for general connected POMDPs that obtain near optimal average reward. One algorithm we present has a convergence rate which depends exponentially on a certain horizon time of an optimal policy, but has no dependence on the number of (unobservable) states. The main building block of our algorithms is an implementation of an approximate reset strategy, which we show always exists in every POMDP. An interesting aspect of our algorithms is how they use this strategy when balancing exploration and exploitation.