# Distributed function estimation: adaptation using minimal communication

arXiv: https://arxiv.org/abs/2003.12838 · HTML: https://mlsanity.com/paper/2003.12838/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Mar 2020.

## Built on by (most cited first, 6 of 6)

- [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)
- [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)

## Abstract (arXiv)

We investigate whether in a distributed setting, adaptive estimation of a smooth function at the optimal rate is possible under minimal communication. It turns out that the answer depends on the risk considered and on the number of servers over which the procedure is distributed. We show that for the L_∞-risk, adaptively obtaining optimal rates under minimal communication is not possible. For the L2-risk, it is possible over a range of regularities that depends on the relation between the number of local servers and the total sample size.