A PAC algorithm in relative precision for bandit problem with costly sampling

This paper considers the problem of maximizing an expectation function over a finite set, or finite-arm bandit problem. We first propose naive stochastic algorithm for obtaining probably approximately correct (PAC) solution to this discrete optimization in relative precision, that is which solves up error smaller than prescribed tolerance, with high probability. also adaptive provides PAC-solution same guarantees. The outperforms mean complexity terms number generated samples and particularly well suited applications sampling cost.