For one-bit distributed mean estimation with unknown variance, a two-round adaptive protocol achieves the optimal asymptotic MSE, and for many log-concave distributions no non-adaptive protocol can match it.
Inference under Information Constraints I : Lower Bounds from Chi-Square Contraction , 2020 a
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One-Bit Distributed Mean Estimation with Unknown Variance
For one-bit distributed mean estimation with unknown variance, a two-round adaptive protocol achieves the optimal asymptotic MSE, and for many log-concave distributions no non-adaptive protocol can match it.