arXiv:2609. 08564v1 Announce Type: cross Abstract: We study distributed one-dimensional mean estimation under a 1-bit communication constraint.
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We study distributed one-dimensional mean estimation under a 1-bit communication constraint. Each agent observes one sample, drawn independently from an unknown distribution, and returns a single bit in response to a query $Q: \mathbb{R}\to\{0,1\}$ chosen by a central learner.
arXiv:2608. 02538v1 Announce Type: cross Abstract: This paper is concerned with one-bit mean estimation, where each independent sample is represented by a single binary message.
arXiv:2607. 02896v1 Announce Type: cross Abstract: We ask whether interaction is necessary for order-optimal 1-bit mean estimation over nonparametric finite-moment classes.
The paper revisits realizable multiclass PAC learning with bandit feedback, correcting a previously claimed lower bound on sample complexity. It introduces a new anchored dimension, “aBDS,” and establishes a constant‑free three‑part lower bound, while also providing tighter upper bounds that eliminate dependence on the total label count. The authors demonstrate that the optimal sample complexity can vary dramatically even among classes with identical dimensional profiles, revealing a confidence direct‑sum phenomenon and a rank‑saturation phase transition.
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