Finite Budget Allocation Improvement in Ranking and Selection

This paper introduces a new perspective on the problem of finite sample Ranking and Selection. An asymptotically equivalent approximation to the probability of correct selection in terms of power series is derived beyond the classic large deviations principle that has been widely adopted for the design and measurement of allocation policies. The novel approximation method provides more information on the finite sample performance of allocation policies, based on which a new finite computing budget allocation policy is proposed. The asymptotically equivalent approximation may also serve as an estimate of policy performance after allocating the samples. We develop a simple finite computing budget allocation policy based on our approximation and carry out experiments in various settings to show its superiority.