Slowly Changing Adversarial Bandit Algorithms are Efficient for Discounted MDPs
This provides a theoretical framework for applying bandit algorithms to reinforcement learning, which is incremental as it builds on existing adversarial bandit methods.
The paper tackles the problem of reducing discounted infinite-horizon reinforcement learning to multi-armed bandits by placing independent bandit learners in each state, showing that slowly changing adversarial bandit algorithms can achieve optimal expected regret under ergodicity and fast mixing assumptions.
Reinforcement learning generalizes multi-armed bandit problems with additional difficulties of a longer planning horizon and unknown transition kernel. We explore a black-box reduction from discounted infinite-horizon tabular reinforcement learning to multi-armed bandits, where, specifically, an independent bandit learner is placed in each state. We show that, under ergodicity and fast mixing assumptions, any slowly changing adversarial bandit algorithm achieving optimal regret in the adversarial bandit setting can also attain optimal expected regret in infinite-horizon discounted Markov decision processes, with respect to the number of rounds $T$. Furthermore, we examine our reduction using a specific instance of the exponential-weight algorithm.