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# The Sample-Complexity of General Reinforcement Learning

*Proceedings of the 30th International Conference on Machine Learning*, PMLR 28(3):28-36, 2013.

#### Abstract

We study the sample-complexity of reinforcement learning in a general setting without assuming ergodicity or finiteness of the environment. Instead, we define a topology on the space of environments and show that if an environment class is compact with respect to this topology then finite sample-complexity bounds are possible and give an algorithm achieving these bounds. We also show the existence of environment classes that are non-compact where finite sample-complexity bounds are not achievable. A lower bound is presented that matches the upper bound except for logarithmic factors.