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In this paper, we study the pure exploration bandit model on generaldistribution functions, which means that the reward function of each armdepends on the whole distribution, not only its mean. We adapt the racingframework and LUCB framework to solve this problem, and design algorithms forestimating the value of the reward functions with different types ofdistributions. Then we show that our estimation methods have correctnessguarantee with proper parameters, and obtain sample complexity upper bounds forthem. Finally, we discuss about some important applications and theircorresponding solutions under our learning framework.

Pure Exploration Bandit Problem with General Reward Functions Depending on Full Distributions