Non-Adaptive 1-Bit Mean Estimation: Minimax Rates and the Sample-Interval Tradeoff
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 $[-λ,λ]$ and $k$-th central moment at most $σ^k$, 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 (a...
| Authors | Ivan Lau, Jonathan Scarlett |
|---|---|
| Primary category | stat.ML |
| Published | 8 September 2026 |
| Last updated at source | 8 September 2026 |
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