I have a problem similar to the 'Bernoulli bandit' problem in the exploration-exploitation paradigm, but without the exploitation element.
In particular, I have many levers that I can pull and each pull either succeeds or fails a proportion of the time that is fixed but unknown, and different for each lever. I want to find the lever that succeeds the most often. What's a good strategy to use if I want to minimise the expected number of pulls until I'm 99% sure I've found the one with the highest proportion of successes?
This differs from the usual multi-armed bandit problem in that during this testing I'm not rewarded for getting successes rather than failures. So I don't particularly favour strategies which get more successes. In particular I tried Thompson Sampling and I found that once it had found a good lever it spent too much time pulling that lever and not enough time trying to rule out the second best possibilities.
What would be a good algorithm for this problem? Can we say what would be optimal from a Bayesian perspective?