DADAO is a novel decentralized asynchronous stochastic algorithm to minimize a sum of $L$-smooth and $\mu$-strongly convex functions distributed over a time-varying connectivity network of size $n$. We model the local gradient updates and gossip communication procedures with separate independent Poisson Point Processes, decoupling the computation and communication steps in addition to making the whole approach completely asynchronous. Our method employs primal gradients and do not use a multi-consensus inner loop nor other ad-hoc mechanisms as Error Feedback, Gradient Tracking or a Proximal operator. By relating spatial quantities of our graphs $\chi^*_1,\chi_2^*$ to a necessary minimal communication rate between nodes of the network, we show that our algorithm requires $\mathcal{O}(n\sqrt{\frac{L}{\mu}}\log \epsilon)$ local gradients and only $\mathcal{O}(n\sqrt{\chi_1^*\chi_2^*}\sqrt{\frac{L}{\mu}}\log \epsilon)$ communications to reach a precision $\epsilon$. If SGD with uniform noise $\sigma^2$ is used, we reach a precision $\epsilon$ with same speed, up to a bias term in $\mathcal{O}(\frac{\sigma^2}{\sqrt{\mu L}})$. This improves upon the bounds obtained with current state-of-the-art approaches, our simulations validating the strength of our relatively unconstrained method. Our source-code is released on a public repository.
翻译:DADO 是一个新颖的分散式零碎分析算法, 以最大限度地减少在时间变化的连接网络中分布的美元- mooth 和 $\mua- 坚固的 convex 函数。 我们用独立独立的 Poisson Point 进程模拟本地梯度更新和八卦通信程序, 将计算和通信步骤分离, 使整个方法完全不同步。 我们的方法使用原始梯度, 并且不使用多一致内环或其他机制作为错误反馈、 梯度跟踪或Proximal 操作器。 我们的图表的空间数量 $\ chi% 1,\ chi_ 2 $ 和网络节点之间必要的最低通信率。 我们的算法需要$\ macal{ O} (n\ mulog ) 本地梯度 $ (musmusl) 本地梯度值, 并且只有$\ mathclor_ commal_ $_ laxal_ laus a ral_ ral_ lium_ lax_ laus a gal_ lass dal_ dal_ dal_ laus dal_ rus dal_ laus a_ lax_ lax dal_ lax_ disl_ laxxxxxxx_ $_ l_ lixxxxxx_____ ligal__ ral__ lixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxal_l_l_l_l_l_l_l_l=xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx