A PAC algorithm in relative precision for bandit problem with costly sampling
This work addresses optimization under uncertainty for scenarios with expensive sampling, offering an incremental improvement in efficiency.
The paper tackles the finite-arm bandit problem by proposing naive and adaptive stochastic bandit algorithms to achieve a probably approximately correct (PAC) solution with relative precision, where the adaptive algorithm reduces sample complexity and is suited for high-cost sampling applications.
This paper considers the problem of maximizing an expectation function over a finite set, or finite-arm bandit problem. We first propose a naive stochastic bandit algorithm for obtaining a probably approximately correct (PAC) solution to this discrete optimization problem in relative precision, that is a solution which solves the optimization problem up to a relative error smaller than a prescribed tolerance, with high probability. We also propose an adaptive stochastic bandit algorithm which provides a PAC-solution with the same guarantees. The adaptive algorithm outperforms the mean complexity of the naive algorithm in terms of number of generated samples and is particularly well suited for applications with high sampling cost.