  In this paper, we study the pure exploration bandit model on general
distribution functions, which means that the reward function of each arm
depends on the whole distribution, not only its mean. We adapt the racing
framework and LUCB framework to solve this problem, and design algorithms for
estimating the value of the reward functions with different types of
distributions. Then we show that our estimation methods have correctness
guarantee with proper parameters, and obtain sample complexity upper bounds for
them. Finally, we discuss about some important applications and their
corresponding solutions under our learning framework.
