Annealed Entropic Allocation for Ranking and Selection

2026-06-09

AI Summary

This work addresses the instability caused by hard switching in sequential budget allocation when the objective function is non-smooth—particularly pronounced when candidate alternatives exhibit similar performance. To mitigate this issue, the authors propose an annealed weighted soft-min framework that replaces the original non-smooth minimax large-deviation rate objective with a smooth log-sum-exp surrogate equipped with an annealing mechanism. This approach is further enhanced by a saddlepoint approximation correction derived from refined tail asymptotics. The resulting method achieves smooth and stable budget allocation while preserving first-order large-deviation optimality. Experimental results demonstrate that the proposed algorithm significantly outperforms existing methods in both Gaussian and exponential settings, with especially notable gains when the performance of competing alternatives is closely matched.

Abstract

We propose Annealed Entropic Allocation, an annealed weighted soft-min framework for sequential budget allocation in ranking and selection. The central idea is to replace the non-smooth maximin large-deviation rate objective with a weighted log-sum-exp surrogate that aggregates challenger-specific pairwise scores through soft-min weights, mitigating hard switching when several challengers are nearly active. To improve finite-budget discrimination, we incorporate the saddlepoint approximation -- a sub-exponential correction derived from refined pairwise tail asymptotics. Because these corrections are sub-exponential and the smoothing parameter is annealed to zero, the surrogate preserves the same first-order large-deviation target as the classical maximin formulation. We show that the surrogate converges uniformly to the hard minimum, that the soft-min weights concentrate on the active challengers, and that, under fixed weights, the induced target allocation map is continuous on the simplex interior. Numerical experiments on Gaussian and exponential instances demonstrate competitive performance, especially when multiple challengers are nearly tied.

Problem

• ranking and selection
• sequential allocation
• budget allocation
• large-deviation rate
• nearly tied challengers

Innovation

• annealed entropic allocation
• soft-min surrogate
• saddlepoint approximation
• ranking and selection
• large-deviation rate