Parameter optimization for board game AI

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I've created a small AI program which can play Othello. The algorithmn I use (MCTS UTC) has a parameter where I can tune the exploration vs exploitation ratio. This is a single float value ranging from 0 to 10 (infinity is possible but high values don't make a lot of sense)

I can easily let the algorithm play versus itself with different values of this parameter. This would give me an idea which of the two values is better.

What is a good algorithm to optimize this parameter?

(I prefer an algorithm that has some research or publications to go indepth as to why or when it work best.)

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Consider something on the order of a genetic algorithm where the program plays with itself and the winners ratio is kept, and varied a little. Keep track of the values. Over time it may converge to a 'best' balance.