Series Expansion of Probability of Correct Selection for Improved Finite Budget Allocation in Ranking and Selection
This work addresses the problem of more accurate simulation budget allocation for researchers and practitioners in operations research and decision-making under uncertainty, though it appears incremental as it builds on existing large deviations approximations.
The paper tackles the challenge of improving finite sample performance in Ranking and Selection by developing a Bahadur-Rao type expansion for the Probability of Correct Selection (PCS), which enhances PCS approximation under limited simulation budgets and leads to a novel finite budget allocation policy that achieves superior PCS performance compared to traditional methods in toy examples.
This paper addresses the challenge of improving finite sample performance in Ranking and Selection by developing a Bahadur-Rao type expansion for the Probability of Correct Selection (PCS). While traditional large deviations approximations captures PCS behavior in the asymptotic regime, they can lack precision in finite sample settings. Our approach enhances PCS approximation under limited simulation budgets, providing more accurate characterization of optimal sampling ratios and optimality conditions dependent of budgets. Algorithmically, we propose a novel finite budget allocation (FCBA) policy, which sequentially estimates the optimality conditions and accordingly balances the sampling ratios. We illustrate numerically on toy examples that our FCBA policy achieves superior PCS performance compared to tested traditional methods. As an extension, we note that the non-monotonic PCS behavior described in the literature for low-confidence scenarios can be attributed to the negligence of simultaneous incorrect binary comparisons in PCS approximations. We provide a refined expansion and a tailored allocation strategy to handle low-confidence scenarios, addressing the non-monotonicity issue.