I'm working on implementing a multi-armed-bandit-like approach for determining the best price to offer for a product. Our goal is to optimize profit, meaning, we want to find the price where (price-cost) x number of purchases is greatest. The problem is that there is a known pattern of seasonality within the week. So, if I set the price to the same thing on a Monday vs. a Wednesday, they might have dramatically different volume.

That's my specific situation, but it started me wondering more broadly about using a multi-armed bandit when there are external factors (aside from which "arm" of the bandit you pull) that affects the results you get. Is there a way of taking these factors into account? Perhaps there are results that suggest that if you run the algorithm long enough, it converges in spite of the other factors?