# Maximum Multi-armed Bandit

My problem is similar to the multi-armed bandit problem in that I need to allocate "pulls" between n options, each giving a stochastic real reward and the pulls for a given arm are IID.

Differences:

1. I only get to keep the maximum reward, not all rewards
2. I have a (usually short) history of rewards for each arm
3. I must allocate k pulls all at once in advance and do not get to change them as they are made.

Has this problem been studied? (Note that this is a simplification of another question I wrote)