אסטימציה של תוצאה ממוצעת 1-ביט: קצבים מינימקסימיים והתמורה בין קצב סריג

תקציר מקורי באנגליתarXiv:2609.08564v1 Announce Type: cross Abstract: 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. The distribution has mean in $[-\lambda,\lambda]$ and $k$-th central moment at most $\sigma^k$, for a fixed $k>1$. The order-optimal two-stage protocol of Lau and Scarlett uses responses from the first batch to choose the second-batch queries, motivating the question of whether this single round of interaction is necessary. We answer this negatively: for every $k>1$, a non-adaptive protocol attains the adaptive 1-bit minimax rate (and concurrent works reached the same