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I think that assuming stationary behavior (bad assumption) then given enough time either A will smash B or B will smash A. As in, it's almost impossible that they are exactly equal in performance and given enough impressions even the smallest change will be optimized for.

I think that's a bad thing, though. A single conversion metric optimization is only good for some (large or medium) effect size. After a point, criterions like "I kind of like A" are much more important.

In A/B testing you see this when your ambitious testing campaign returns "insignificant". In MAB you see it when two choices run at roughly 50/50 enrollment for a long period of time.

So on these two extremes, I think practical use of A/B and MAB should be roughly identical. In the middle ground where A is usefully but not incredibly better than B, I feel they must differ.




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