题  目：Stochastic splitting algorithms for nonconvex problems in imaging and data sciences

报告人：张小群

单  位：上海交通大学

时  间：8月12日，上午9:00

地  点：腾讯743-687-844

摘要：Splitting algorithms are largely adopted for composited optimization problems arising in imaging and data sciences. In this talk, I will present stochastic variants of composited optimization algorithms in nonconvex settings and their applications. The first class of algorithms is based on Alternating direction method of multipliers (ADMM) for nonconvex composite problems. In particular, we study the ADMM method combined with a class of variance reduction gradient estimators and established the global convergence of the sequence and convergence rate under the assumption of Kurdyka-Lojasiewicz (KL) function. The efficiency of the algorithms is verified through statistical learning examples and L0 based sparse regularization for 3D image reconstruction. The second class of stochastic algorithm is proposed for a type of three-block alternating minimization arising in training quantized neural networks.  We develop a convergence theory for the stochastic three-block algorithm (STAM) and obtain an $\epsilon$-stationary point with optimal convergence rate $\mathcal{O}(\epsilon^{-4})$. The experiments on training quantized DNNs are carried out on different network structures on CIFAR-10 and CIFAR-100 datasets. The test accuracy indicates the effectiveness of STAM algorithm for training binary quantization DNNs.

报告人简介：张小群, 上海交通大学自然科学研究院和数学科学学院特聘教授。主要研究方向：图像科学、医学图像处理、数据科学等问题中的数学模型与计算方法。现任Inverse problems and Imaging、  CSIAM-AM杂志编委， CSIAM数学大数据与人工智能专委会、数学与医学交叉学科专业委员会委员。