分布式函数估计：使用最少通信的自适应
Distributed function estimation: adaptation using minimal communication
摘要：
我们调查是否在一个分布式的设置，自适应估计的光滑函数在最佳速率下是可能的最小通信。事实证明，答案取决于所考虑的风险以及分发该过程的服务器数量。我们发现，对于$L_\infty$风险，自适应地获得最佳的通信下的速率是不可能的。对于$L_2$ -风险，可能在一定范围内发生，这取决于本地服务器数量与总样本量之间的关系。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
