论文标题
分布式功能估计：使用最小通信的适应
Distributed function estimation: adaptation using minimal communication
论文作者
论文摘要
我们调查在分布式设置中，在最小的通信中，以最佳速度的平滑函数对平滑函数的自适应估计。事实证明，答案取决于所考虑的风险以及分布过程的服务器数量。我们表明，对于$ l_ \ infty $ - 风险，在最小的通信下自适应地获得最佳利率。对于$ L_2 $ - 风险，可以在一系列规律性的范围内取决于本地服务器数量与总样本量之间的关系。
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 $L_\infty$-risk, adaptively obtaining optimal rates under minimal communication is not possible. For the $L_2$-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.
