Distributed nonparametric function estimation: Optimal rate of convergence and cost of adaptation
研究了高斯序列模型和白噪声模型下通信约束的分布式极小化估计和自适应估计，建立了给定贝索夫类上的极小化收敛速率，量化了自适应的通信代价，并构造了最优自适应程序。
Distributed minimax estimation and distributed adaptive estimation under communication constraints for Gaussian sequence model and white noise model are studied. The minimax rate of convergence for distributed estimation over a given Besov class, which serves as a benchmark for the cost of adaptation, is established. We then quantify the exact communication cost for adaptation and construct an optimally adaptive procedure for distributed estimation over a range of Besov classes. The results demonstrate significant differences between nonparametric function estimation in the distributed setting and the conventional centralized setting. For global estimation, adaptation in general cannot be achieved for free in the distributed setting. The new technical tools to obtain the exact characterization for the cost of adaptation can be of independent interest.