# Adaptive distributed methods under communication constraints

arXiv: https://arxiv.org/abs/1804.00864 · HTML: https://mlsanity.com/paper/1804.00864/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2018.

## Built on by (most cited first, 9 of 9)

- [Optimal Federated Learning for Nonparametric Regression with Heterogeneous Distributed Differential Privacy Constraints](https://mlsanity.com/paper/2406.06755/) (2024)
- [Order-Optimal Sequential 1-Bit Mean Estimation in General Tail Regimes](https://mlsanity.com/paper/2604.07796/) (2026)
- [Sequential 1-bit Mean Estimation with Near-Optimal Sample Complexity](https://mlsanity.com/paper/2509.21940/) (2025)
- [Distributed Nonparametric Function Estimation: Optimal Rate of Convergence and Cost of Adaptation](https://mlsanity.com/paper/2107.00179/) (2021)
- [Distributed Sparse Normal Means Estimation with Sublinear Communication](https://mlsanity.com/paper/2102.03060/) (2021)
- [Optimal high-dimensional and nonparametric distributed testing under communication constraints](https://mlsanity.com/paper/2202.00968/) (2022)
- [Distributed Nonparametric Estimation under Communication Constraints](https://mlsanity.com/paper/2204.10373/) (2022)
- [Adaptive Resolution for Finite-Rank Gaussian Processes](https://mlsanity.com/paper/2505.24066/) (2025)
- [Distributed Sparse Linear Regression under Communication Constraints](https://mlsanity.com/paper/2301.04022/) (2023)

## Abstract (arXiv)

We study distributed estimation methods under communication constraints in a distributed version of the nonparametric random design regression model. We derive minimax lower bounds and exhibit methods that attain those bounds. Moreover, we show that adaptive estimation is possible in this setting.