论文标题
用于大规模分布式多代理优化的通信有效的准牛顿法
A Communication Efficient Quasi-Newton Method for Large-scale Distributed Multi-agent Optimization
论文作者
论文摘要
我们提出了一种用于大型多代理凸复合优化的通信有效的准牛顿法。我们假设设置了一个合作解决全球最小化问题的代理网络，并强烈凸出局部成本功能，并通过非平滑凸正则使用者增强。通过引入共识变量，我们获得了一个块 - 二基因HESSIAN，因此在近似客观曲率信息时消除了对额外通信的需求。此外，我们通过存储$ c $ c $ dimension $ d $的向量，从$ \ mathcal {o}（d^3）$从$ \ mathcal {o}（d^3）$降低现有的二级准牛顿方法的计算成本。提出了一种异步实现，以消除协调的需求。建立了预期中的全局线性收敛率，我们使用实际数据集以数值来证明我们的算法的优点。
We propose a communication efficient quasi-Newton method for large-scale multi-agent convex composite optimization. We assume the setting of a network of agents that cooperatively solve a global minimization problem with strongly convex local cost functions augmented with a non-smooth convex regularizer. By introducing consensus variables, we obtain a block-diagonal Hessian and thus eliminate the need for additional communication when approximating the objective curvature information. Moreover, we reduce computational costs of existing primal-dual quasi-Newton methods from $\mathcal{O}(d^3)$ to $\mathcal{O}(cd)$ by storing $c$ pairs of vectors of dimension $d$. An asynchronous implementation is presented that removes the need for coordination. Global linear convergence rate in expectation is established, and we demonstrate the merit of our algorithm numerically with real datasets.
