We consider the problem of federated learning in a one-shot setting in which there are $m$ machines, each observing $n$ samples function from an unknown distribution on non-convex loss functions. Let $F:[-1,1]^d\to\mathbb{R}$ be the expected loss function with respect to this unknown distribution. The goal is to find an estimate of the minimizer of $F$. Based on its observations, each machine generates a signal of bounded length $B$ and sends it to a server. The sever collects signals of all machines and outputs an estimate of the minimizer of $F$. We propose a distributed learning algorithm, called Multi-Resolution Estimator for Non-Convex loss function (MRE-NC), whose expected error is bounded by $\max\big(1/\sqrt{n}(mB)^{1/d}, 1/\sqrt{mn}\big)$, up to polylogarithmic factors. We also provide a matching lower bound on the performance of any algorithm, showing that MRE-NC is order optimal in terms of $n$ and $m$. Experiments on synthetic and real data show the effectiveness of MRE-NC in distributed learning of model's parameters for non-convex loss functions.

翻译：我们考虑的是在一个一拍的环境下进行联合学习的问题,即机器有美元美元,每个在一拍的环境下,每个观察单位都从一个未知的非碳流损失函数的分布不明的分布上观测美元样本功能。让美元[1,1,1,d\to\\mathb{R}R}]作为这一未知分布的预期损失函数。我们考虑的是,在一拍的环境下,联合学习的问题。我们考虑的是,在一个一拍的环境下,在每台机器有1美元机器,每台机器都用1美元来观测,在每台机器有1美元限制长度的信号,并将它发送到一个服务器上。在任何算法的性能上收集了所有机器和产出的信号,估算了美元最小值的估计数。我们提出一个分布式学习算法,称为“非Cononfex损失函数(MRE-NC)的多分辨率模拟模拟模拟模拟算算法,其预期的错误受$max ASim lex ASimal as lex am am legent am and am asimal- legnimalmamax lem lemlemlemlem lem lem lem lem lem lemlemlemlemlemlemlemlemlemlem lem lem lem lem lem lem lem lem lemlemlemlemal lem lemal lem lemal lemlem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem lem