并行采样中超越确定性自适应性的随机化
Randomization Beyond Deterministic Adaptivity in Parallel Sampling
- School of Computer Science and Technology, Dalian University of Technology（大连理工大学计算机科学与技术学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究证明在并行采样中，随机化调度可超越确定性自适应策略，以指数小散度逼近目标，仅需两个随机比特，并在维度389处建立分离。
AI中文摘要：
我们研究并行采样器，每个坐标仅揭示一次，且每个批次的坐标根据其精确的条件边际独立抽取。在相同的采样接口和硬性三轮上限下，随机化可以超越任何根据先前观测值自适应调整批次的确定性策略的精度。对于一个显式的全支撑二元族，最优确定性自适应前向Kullback-Leibler散度随维度线性增长，而四个固定调度的均匀混合则具有指数小的散度。仅需两个独立的公平比特即可选择调度。我们确定了确定性最优中的渐近加性常数，并证明其最优总变差趋于四分之一。一个向外舍入的有限和证书在维度389处建立了散度分离。该机制结合了不可逆的首批依赖损失与随机化组件中的后验集中。一个密度覆盖引理描述了它们的混合如何恢复目标。一个互补的噪声匹配族展示了非自适应调度的轮次差距增长，尽管均匀随机坐标顺序仍具有线性混合误差。这些结果涉及已知的有限结构和精确的条件边际。
英文摘要：
We study parallel samplers that reveal each coordinate once and draw the coordinates of each batch independently from their exact conditional marginals. Under the same sampling interface and a hard three-round cap, randomization can improve accuracy beyond every deterministic policy that adapts its batches to previously observed values. For an explicit full-support binary family, the optimal deterministic adaptive forward Kullback-Leibler divergence grows linearly with the dimension, while a uniform mixture of four fixed schedules has exponentially small divergence. Only two independent fair bits are needed to select the schedule. We determine the asymptotic additive constant in the deterministic optimum and show that its optimal total variation tends to one quarter. An outward-rounded finite-sum certificate establishes divergence separation at dimension 389. The mechanism combines an irreversible first-batch dependence loss with posterior concentration in the randomized components. A density-coverage lemma describes how their mixture restores the target. A complementary noisy-matching family exhibits a growing round gap for nonadaptive schedules, although uniform random coordinate order still has linear mixture error. These results concern known finite structures and exact conditional marginals.
