发表机构
Hanoi University of Science and Technology; Quantum AI & Cyber Security Institute, FPT Corporation（河内科技大学; FPT公司量子人工智能与网络安全研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对1比特反馈下的固定置信度最佳臂识别，提出基于随机阈值查询的均值估计原语，并嵌入候选-挑战者算法，实现间隙自适应样本复杂度，且证明对数惩罚下界。
AI 中文摘要
我们研究在严格1比特反馈约束下的固定置信度最佳臂识别问题。在每一轮中，学习器选择一个臂和一个查询集，仅接收一个比特，指示采样奖励是否属于该集合。我们考虑一个无分布假设的有限方差设置，并采用逐臂局部化方法，其中直接的经验均值估计不再可用，截断变得不可避免。我们首先基于随机化阈值查询和截断尾部积分恒等式，提出一个时间均匀的1比特均值估计原语。然后，我们将该原语嵌入到候选-挑战者最佳臂识别算法中。一个固定截断算法提供了简单的任意时间$(\epsilon,\delta)$-PAC保证，而一个分阶段自适应截断算法将截断水平与当前分辨率匹配，并产生间隙自适应的样本复杂度。我们还证明了一个$K$臂最坏情况信息论下界，表明有限方差1比特反馈引起的对数惩罚是内在的。该下界与分阶段算法的主导项匹配，直到低阶$\log\log$因子。
英文摘要
We study fixed-confidence best-arm identification under strict 1-bit feedback constraints. At each round, the learner selects an arm and a query set, and receives only a single bit indicating whether the sampled reward belongs to that set. We consider a distribution-free finite-variance setting with arm-wise localization, where direct empirical mean estimation is no longer available and clipping becomes unavoidable. We first formulate a time-uniform 1-bit mean-estimation primitive based on randomized threshold queries and a clipped tail-integral identity. We then embed this primitive into candidate-challenger best-arm identification algorithms. A fixed-clipping algorithm gives a simple anytime $(ε,δ)$-PAC guarantee, while a phased adaptive-clipping algorithm matches the clipping level to the current resolution and yields a gap-adaptive sample complexity. We also prove a $K$-arm worst-case information-theoretic lower bound showing that the logarithmic penalty caused by finite-variance 1-bit feedback is intrinsic. This bound matches the leading dependence of the phased algorithm up to lower-order $\log\log$ factors.
CommentsTo appear in Advances in Neural Information Processing Systems 39 (NeurIPS 2026, Spotlight)
