A Multi-Armed Bandit Approach for Online Expert Selection in Markov Decision Processes
For reinforcement learning practitioners needing to select among pre-trained policies online, this provides a principled regret-bounded approach.
The paper formulates expert selection in MDPs as a multi-armed bandit problem, proposes an adapted UCB algorithm, and proves logarithmic regret. Validation on a small MDP shows the theory holds.
We formulate a multi-armed bandit (MAB) approach to choosing expert policies online in Markov decision processes (MDPs). Given a set of expert policies trained on a state and action space, the goal is to maximize the cumulative reward of our agent. The hope is to quickly find the best expert in our set. The MAB formulation allows us to quantify the performance of an algorithm in terms of the regret incurred from not choosing the best expert from the beginning. We first develop the theoretical framework for MABs in MDPs, and then present a basic regret decomposition identity. We then adapt the classical Upper Confidence Bounds algorithm to the problem of choosing experts in MDPs and prove that the expected regret grows at worst at a logarithmic rate. Lastly, we validate the theory on a small MDP.