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Online reinforcement learning (RL) has been widely applied in informationprocessing scenarios, which usually exhibit much uncertainty due to theintrinsic randomness of channels and service demands. In this paper, weconsider an un-discounted RL in general Markov decision processes (MDPs) withboth endogeneous and exogeneous uncertainty, where both the rewards and statetransition probability are unknown to the RL agent and evolve with the time aslong as their respective variations do not exceed certain dynamic budget (i.e.,upper bound). We first develop a variation-aware Bernstein-based upperconfidence reinforcement learning (VB-UCRL), which we allow to restartaccording to a schedule dependent on the variations. We successfully overcomethe challenges due to the exogeneous uncertainty and establish a regret boundof saving at most $\sqrt{S}$ or $S^{\frac{1}{6}}T^{\frac{1}{12}}$ compared withthe latest results in the literature, where $S$ denotes the state size of theMDP and $T$ indicates the iteration index of learning steps.

Fundamental Limits of Reinforcement Learning in Environment with Endogeneous and Exogeneous Uncertainty