探究1比特均值估计中交互是否必要，揭示单次自适应查询的最优性。
Open Problem: Is Interaction Necessary for Order-Optimal 1-bit Mean Estimation?
- 提出仅需一次自适应转换的非自适应量化协议，实现最优速率。
- 证明任意非自适应量化器无法达到自适应方法的最优率。
- 解答非参数有限矩类下1比特均值估计的最优性边界问题。
我们探讨在非参数有限矩类中，1比特均值估计是否需要交互。自适应阈值查询协议可实现阶最优的1比特极小极大率，且仅需一次自适应转换（即两阶段查询）即可达成相同速率。在非自适应设置下，已知阈值和区间查询表现严重次优，但任意非自适应量化器的性能仍未知。此类量化器能否匹配自适应速率，实现最优单次协议？抑或已知的两阶段估计器已达最优，单次自适应转换既是必要也是充分条件？
原文摘要 · Abstract (English)
We ask whether interaction is necessary for order-optimal 1-bit mean estimation over nonparametric finite-moment classes. Adaptive threshold-query protocols achieve the order-optimal 1-bit minimax rate, and the same rate is attainable with general 1-bit queries using only one adaptive transition (i.e., two stages of querying). In the non-adaptive setting, threshold and interval queries are known to be highly suboptimal, but the case of arbitrary non-adaptive quantizers remains unresolved. Can such quantizers match the adaptive rate, yielding an optimal one-shot protocol? Or is the known two-stage estimator stage-optimal, with a single adaptive transition being necessary and sufficient?
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