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.

翻译：我们提出退火熵分配（Annealed Entropic Allocation），一种用于排序与选择中顺序预算分配的退火加权软最小框架。核心思想是将非光滑的最大-最小大偏差率目标函数替换为加权对数-求和-指数代理函数，该函数通过软最小权重聚合竞争者的成对得分，从而在多个竞争者接近活跃时缓解硬切换。为提升有限预算下的判别能力，我们引入鞍点近似——一种基于精细化成对尾部渐近性的亚指数修正。由于这些修正为亚指数形式且平滑参数随退火过程趋近于零，该代理函数保留了与经典最大-最小公式相同的一阶大偏差目标。我们证明：代理函数一致收敛于硬最小值；软最小权重集中于活跃竞争者；在固定权重下，诱导的目标分配映射在单纯形内部连续。针对高斯与指数分布实例的数值实验表明，该方法在多个竞争者结果接近时具有竞争性表现。