Online Learning in Markov Decision Processes with Arbitrarily Changing Rewards and Transitions

We consider decision-making problems in Markov decision processes where both the rewards and the transition probabilities vary in an arbitrary (e.g., non-stationary) fashion. We present algorithms that combine online learning and robust control, and establish guarantees on their performance evaluated in retrospect against alternative policies-i.e., their regret. These guarantees depend critically on the range of uncertainty in the transition probabilities, but hold regardless of the changes in rewards and transition probabilities over time. We present a version of the main algorithm in the setting where the decision-maker's observations are limited to its trajectory, and another version that allows a trade-off between performance and computational complexity.