# Mapping given probabilities to empirical probabilities

Consider following problem statement:

You have given $$n$$ actions. You can perform any of them. Each action gives you success with some probability. The challenge is to perform given finite number of actions to get maximum successes.

Here, we can perform actions and slowly decide upon possible probabilities of each action for success. I have no doubts in this problem.

Now consider following variant of the problem:

You have given $$n$$ actions. You can perform any of them. Each action gives you success with some probability. Also you are given set of $$n$$ probabilities, but you are not told which probability is associated with which action. The challenge is to utilise this additional information to perform given finite number of actions to get maximum successes.

I have doubt in this problem that how we can map probabilities to actions? I can do some enough number of actions to gather empirical probability and them try to associate given probabilties with actions having closest empirical probabities. But, is there any algorithm for such problem in the literature?

• I ampreety sure you can modify the UCB method for this problem. Just check how UCB is derived in the first place.
– user9947
Feb 21 at 7:36