Multi armed bandits and quantum channel oracles

Multi armed bandits are one of the theoretical pillars of reinforcement learning. Recently, the investigation of quantum algorithms for multi armed bandit problems was started, and it was found that a quadratic speed-up is possible when the arms and the randomness of the rewards of the arms can be queried in superposition. Here we introduce further bandit models where we only have limited access to the randomness of the rewards, but we can still query the arms in superposition. We show that this impedes any speed-up of quantum algorithms.