论文标题
Dino：分布式牛顿型优化方法
DINO: Distributed Newton-Type Optimization Method
论文作者
论文摘要
我们提出了一种在分布式计算环境上进行有限和优化的新型牛顿型牛顿型算法。我们的名为Dino的方法克服了类似现有方法的理论和实际缺点。在最小的假设下，我们保证Dino与一般非凸功能的一阶固定点和网络上任意数据分布的全局子线性收敛。此外，对于满足Polyak-lojasiewicz（PL）不平等的功能，我们表明Dino具有线性收敛速率。我们提出的算法实际上是无参数的，因为无论选定的超参数易于调整，它都会收敛。此外，其子问题是简单的线性最小二乘，为其有效的求解器。与类似替代方案相比，数值模拟证明了恐龙的效率。
We present a novel communication-efficient Newton-type algorithm for finite-sum optimization over a distributed computing environment. Our method, named DINO, overcomes both theoretical and practical shortcomings of similar existing methods. Under minimal assumptions, we guarantee global sub-linear convergence of DINO to a first-order stationary point for general non-convex functions and arbitrary data distribution over the network. Furthermore, for functions satisfying Polyak-Lojasiewicz (PL) inequality, we show that DINO enjoys a linear convergence rate. Our proposed algorithm is practically parameter free, in that it will converge regardless of the selected hyper-parameters, which are easy to tune. Additionally, its sub-problems are simple linear least-squares, for which efficient solvers exist. Numerical simulations demonstrate the efficiency of DINO as compared with similar alternatives.
