| Summary: | We consider un-discounted reinforcement learning (RL) in Markov decision processes (MDPs)
under drifting non-stationarity, i.e., both the reward and state transition distributions are allowed
to evolve over time, as long as their respective
total variations, quantified by suitable metrics, do
not exceed certain variation budgets. We first
develop the Sliding Window Upper-Confidence
bound for Reinforcement Learning with Confidence Widening (SWUCRL2-CW) algorithm, and
establish its dynamic regret bound when the variation budgets are known. In addition, we propose
the Bandit-over-Reinforcement Learning (BORL)
algorithm to adaptively tune the SWUCRL2-CW
algorithm to achieve the same dynamic regret
bound, but in a parameter-free manner, i.e., without knowing the variation budgets. Notably, learning non-stationary MDPs via the conventional optimistic exploration technique presents a unique
challenge absent in existing (non-stationary) bandit learning settings. We overcome the challenge
by a novel confidence widening technique that
incorporates additional optimism.
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