Accelerated distributed stochastic optimization methods and applications in machine learning

机器学习，特别是深度学习，在包括人脸识别、数字图像分类、自然语言处理、自动驾驶汽车和科学计算在内的广泛应用中变得越来越有影响力。深度学习的成功在很大程度上取决于大量数据的可用性。一方面，这种“大”数据能够成功学习数据的底层分布，因此学习的模型可以对遵循类似分布的新数据点产生高预测精度。另一方面，大量的数据在设计有效的数值方法时提出了巨大的挑战。该项目的重点是从计算和数学的角度解决由可能包含私人信息的分布式“大”数据所带来的挑战。该项目的研究成果将被纳入研究生课程，本科生和研究生将接受该领域的培训并参与这项研究，每周将组织一次研讨会，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，以及解决有能力处理耦合约束的分散式多智能体优化问题。主要目标是设计快速收敛和通信高效的优化方法，并为解决大规模分布式机器学习问题提供理论保证。针对分布式复合光滑随机问题设计了加速压缩邻近随机梯度方法，针对分布式非凸非光滑问题设计了加速压缩随机次梯度方法，针对非线性耦合约束的多智能体优化设计了最优分散随机梯度方法，该奖项反映了NSF的法定使命，并已被认为是值得通过评估使用的支持基金会的学术价值和更广泛的影响审查标准。

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.