Reinforcement approaches are certainly interesting, but one of the things missing here (and in most A/B stuff) is statistical significance and experimental power. If you have enough data, there are hand wavey arguments that this will eventually be right, but in the meanwhile, if there is some opportunity cost (say, imagine this is a trading algo trying to profit from bid/ask), you screwed yourself out of some unknown amount of profits. There actually ways of hanging a confidence interval on this approach which virtually nobody outside the signal processing and information theory communities know about. Kind of a shame.