TL;DR
A fully non-adaptive protocol whose query list is fixed before any bit is observed and whose sample complexity matches the adaptive one-bit minimax rate in every moment regime.
A randomized fully non-adaptive protocol is constructed that fixes all queries before observing the data and matches the optimal adaptive sample complexity, giving a negative answer to the COLT 2026 open problem asking whether interaction is necessary for order-optimal one-bit mean estimation.
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,\l...
A fully non-adaptive public-coin protocol that fixes every measurable 1-bit query before communication is constructed, and rates answer the Lau--Scarlett open problem for arbitrary measurable 1-bit queries in the affirmative.
Low-Pathwidth GRAND (LP-GRAND) is developed for binary phase-shift keying (BPSK) with precision matrix $Q, and induces an ML codeword for any nonempty binary codebook with equiprobable codewords.
We develop a one-shot (finite-blocklength) channel-coding framework based on the pairwise error probability (PEP) of a decoder with randomized tie-breaking. The tie-breaking rule yields a probability-integral-transform identity: the induced error spectrum describes both random-coding achievability and exact fixed-code...
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