Actually, Chris, I think you misunderstand my comment. Thompson sampling (and Bayesian Bandits in general) can be applied with a model for estimating conversio

Actually, Chris, I think you misunderstand my comment. Thompson sampling (and Bayesian Bandits in general) can be applied with a model for estimating conversion that is more complex than P(conversion|A). It can include parameters for time of day, day of week and even be non-parametric. If you do this, you the standard Thompson sampling framework with nochanges* whatsoever will still kill losers quickly (if the loss is big enough that seasonality cannot save it) and will also wait until it has enough data seasonally to make more refined decisions. This is very different from simply waiting for an even season point to make decisions. You do need more data to understand a more complex world, but having an optimal inference engine to help is better than having a severely sub-optimal engine.