With the rise of the processing power of networked agents in the last decade, second-order methods for machine learning have received increasing attention. To solve the distributed optimization problems over multiagent systems, Newton’s method has the benefits of fast convergence and high estimation accuracy. In this article, we propose a reinforced network Newton method with KK -order control flexibility (RNN-K) in a distributed manner by integrating the consensus strategy and the latest knowledge across the network into local descent direction. The key component of our method is to make the best of intermediate results from the local neighborhood to learn global knowledge, not just for the consensus effect like most existing works, including the gradient descent and Newton methods as well as their refinements. Such a reinforcement enables revitalizing the traditional iterative consensus strategy to accelerate the descent of the Newton direction. The biggest difficulty to design the approximated Newton descent in distributed settings is addressed by using a special Taylor expansion that follows the matrix splitting technique. Based on the truncation on the Taylor series, our method also presents a tradeoff effect between estimation accuracy and computation/communication cost, which provides the control flexibility as a practical consideration. We derive theoretically the sufficient conditions for the convergence of the proposed RNN-K method of at least a linear rate. The simulation results illustrate the performance effectiveness by being applied to three types of distributed optimization problems that arise frequently in machine-learning scenarios.

中文翻译：

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RNN-K：一种基于共识的分布式优化和多智能体系统控制的强化牛顿法


随着过去十年网络代理处理能力的提高，机器学习的二阶方法受到越来越多的关注。针对多智能体系统的分布式优化问题，牛顿法具有收敛速度快、估计精度高等优点。在本文中，我们通过将共识策略和整个网络的最新知识整合到局部下降方向中，以分布式方式提出了一种具有 KK 阶控制灵活性的强化网络牛顿方法（RNN-K）。我们方法的关键组成部分是充分利用局部邻域的中间结果来学习全局知识，而不仅仅是像大多数现有工作那样的共识效果，包括梯度下降和牛顿方法及其改进。这种强化能够重振传统的迭代共识策略，以加速牛顿方向的下降。在分布式设置中设计近似牛顿下降法的最大困难是通过使用遵循矩阵分裂技术的特殊泰勒展开式来解决的。基于泰勒级数的截断，我们的方法还提出了估计精度和计算/通信成本之间的权衡效果，这提供了控制灵活性作为实际考虑。我们从理论上推导了所提出的至少线性速率的 RNN-K 方法收敛的充分条件。仿真结果通过应用于机器学习场景中经常出现的三类分布式优化问题来说明性能有效性。