source: arxiv statistics ml: annealed entropic allocation for ranking and selection
level: research
ranking and selection problems often use a maximin large-deviation rate to allocate simulation budget sequentially. the classical approach picks the alternative with the smallest gap to the best, but this hard switching can be unstable when several alternatives are nearly tied. annealed entropic allocation replaces the non-smooth maximin with a weighted log-sum-exp surrogate. this soft-min aggregation uses challenger-specific pairwise scores, smoothing the allocation and reducing abrupt changes.
the method adds a saddlepoint approximation, a sub-exponential correction from refined pairwise tail asymptotics, to improve discrimination with limited budget. as the smoothing parameter is annealed to zero, the surrogate keeps the same first-order large-deviation target as the original maximin. the soft-min weights concentrate on the active challengers, and the surrogate converges uniformly to the hard minimum. under fixed weights, the allocation rule remains consistent with the asymptotic goals of ranking and selection.
the framework is designed for sequential budget allocation where simulation runs are costly. by avoiding hard switching, it can lead to more stable and efficient use of computational resources. the theoretical guarantees show that the annealing process preserves optimal large-deviation properties while the saddlepoint correction sharpens finite-sample performance. this makes the method suitable for practical simulation optimization tasks where identifying the best system quickly is critical.
why it matters: it offers a more stable and efficient way to allocate simulation budget in ranking and selection, which is useful for data scientists optimizing complex systems with limited computational resources.
source: arxiv statistics ml: annealed entropic allocation for ranking and selection