Accelerated distributed stochastic optimization methods and applications in machine learning

机器学习，特别是深度学习，在人脸识别、数字图像分类、自然语言处理、自动驾驶车辆和科学计算等广泛应用中的影响越来越大。深度学习的成功在很大程度上取决于海量数据的可用性。一方面，这种“大数据”能够成功地学习数据的基本分布，因此学习的模型可以对遵循相似分布的新数据点产生很高的预测精度。另一方面，海量的数据给设计有效的数值方法带来了巨大的挑战。该项目的重点是从计算和数学角度解决分布式“大数据”所带来的挑战，这些数据可能包含私人信息。该项目的研究成果将纳入研究生级别的专题课程，本科生和研究生将接受这一领域的培训并参与这项研究，并将每周组织一次研讨会，以交流与该项目相关的想法。将开发新的计算方法，用于在计算节点集群上训练机器学习模型，以及解决具有处理耦合约束能力的分散多代理优化问题。其主要目标是设计快速收敛和通信高效的优化方法，为解决大规模分布式机器学习问题提供理论保证。加速压缩近似随机梯度法将被设计用于分布式复合光滑随机问题，加速压缩随机次梯度法将被设计用于分布式非凸非光滑问题，最优分散随机梯度法将被设计用于求解具有非线性耦合约束的多智能体优化，并且将在所提出的方法中执行异步实现以获得较高的并行化速度。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响评估标准被认为是值得支持的。

Machine learning, and in particular, deep learning, has become increasingly impactful in a wide range of applications, including face recognition, digital image classification, natural language processing, self-driving vehicles, and scientific computing. The success of deep learning largely depends on the availability of a huge amount of data. This "big" data, on one hand, enables successful learning of the underlying distributions of the data, and thus the learned model can yield high prediction accuracy on new data points that follow similar distributions. On the other hand, the huge amount of data raises great challenges when designing efficient numerical approaches. This project focuses on addressing the challenges that are caused by distributed "big" data that can contain private information, from the computational and mathematical perspectives. Research findings from this project will be included in graduate-level topics courses, undergraduate and graduate students will be trained in this field and will participate in this research, and a weekly seminar will be organized to exchange ideas relevant to this project. New computational approaches will be developed for training machine learning models on a cluster of computing nodes as well as solving decentralized multi-agent optimization problems that have the capacity to handle coupling constraints. The main goal is to design fast-convergent and communication-efficient optimization methods with theoretical guarantees for solving large-scale distributed machine learning problems. Accelerated compressed proximal stochastic gradient methods will be designed for distributed composite smooth stochastic problems, accelerated compressed stochastic subgradient methods will be designed for distributed nonconvex nonsmooth problems, optimal decentralized stochastic gradient methods will be designed for solving multi-agent optimization with nonlinear coupling constraints, and asynchronous implementations will be performed in the proposed methods in order to have high parallelization speed up.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.