@InProceedings{pmlr-v336-lau26a,
  title = 	 {Open Problem: Is Interaction Necessary for Order-Optimal 1-bit Mean Estimation?},
  author =       {Lau, Ivan and Scarlett, Jonathan},
  booktitle = 	 {Proceedings of Thirty Ninth Conference on Learning Theory},
  pages = 	 {7123--7128},
  year = 	 {2026},
  editor = 	 {Hanneke, Steve and Lattimore, Tor},
  volume = 	 {336},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {29 Jun--03 Jul},
  publisher =    {PMLR},
  pdf = 	 {https://raw.githubusercontent.com/mlresearch/v336/main/assets/lau26a/lau26a.pdf},
  url = 	 {https://proceedings.mlr.press/v336/lau26a.html},
  abstract = 	 {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?}
}