论文标题
沟通限制下的分布式高斯平均估计：最佳速率和沟通效率算法
Distributed Gaussian Mean Estimation under Communication Constraints: Optimal Rates and Communication-Efficient Algorithms
论文作者
论文摘要
我们研究在决策理论框架中的通信约束下对高斯平均值的分布估计。在单变量和多变量环境中都建立了最小值的收敛速率，这些融合率是交流成本和统计准确性之间的权衡。开发了沟通效率和统计上最佳的程序。在单变量的情况下，只要每台本地机器至少具有一位，最佳速率仅取决于总通信预算。但是，在多元案例中，最小值率取决于当地机器之间通信预算的特定分配。 尽管在常规环境中对高斯平均值的最佳估计相对简单，但在通信约束下，无论是在最佳过程设计还是下限参数方面都涉及。本文开发的技术可能具有独立的兴趣。一个必不可少的步骤是将最小值估计问题分解为两个阶段，即定位和改进。这种关键分解为较低分析和最佳过程设计提供了一个框架。
We study distributed estimation of a Gaussian mean under communication constraints in a decision theoretical framework. Minimax rates of convergence, which characterize the tradeoff between the communication costs and statistical accuracy, are established in both the univariate and multivariate settings. Communication-efficient and statistically optimal procedures are developed. In the univariate case, the optimal rate depends only on the total communication budget, so long as each local machine has at least one bit. However, in the multivariate case, the minimax rate depends on the specific allocations of the communication budgets among the local machines. Although optimal estimation of a Gaussian mean is relatively simple in the conventional setting, it is quite involved under the communication constraints, both in terms of the optimal procedure design and lower bound argument. The techniques developed in this paper can be of independent interest. An essential step is the decomposition of the minimax estimation problem into two stages, localization and refinement. This critical decomposition provides a framework for both the lower bound analysis and optimal procedure design.
