文献类型：期刊文献

英文题名：Implicit Regularization and Entrywise Convergence of Riemannian Optimization for Low Tucker-Rank Tensor Completion

作者：Wang, Haifeng[1,2];Chen, Jinchi[3];Wei, Ke[1]

机构：[1]Fudan Univ, Sch Data Sci, Shanghai, Peoples R China;[2]China Mobile Zhejiang Res & Innovat Inst, Hangzhou, Peoples R China;[3]East China Univ Sci & Technol, Sch Math, Shanghai, Peoples R China

年份：2023

卷号：24

外文期刊名：JOURNAL OF MACHINE LEARNING RESEARCH

收录：;EI(收录号：20250117638048);WOS:【SCI-EXPANDED(收录号:WOS:001130268100001)】；

基金：This work was partially supported by the National Key R&D Program of China (Grant No. 2021YFA1003300) , Natural Science Foundation of Shanghai (Grant No. 23ZR1406400) , and National Science Foundation of China (Grant No. 12001108) .

语种：英文

外文关键词：low rank tensor completion; Tucker decomposition; Riemannian gradient; entrywise convergence; implicit regularization; leave-one-out

摘要：This paper is concerned with the low Tucker-rank tensor completion problem, which is about reconstructing a tensor T is an element of Rnxnxn of low multilinear rank from partially observed entries. Riemannian optimization algorithms are a class of efficient methods for this prob-lem, but the theoretical convergence analysis is still lacking. In this manuscript, we establish the entrywise convergence of the vanilla Riemannian gradient method for low Tucker-rank tensor completion under the nearly optimal sampling complexity O(n3/2). Meanwhile, the implicit regularization phenomenon of the algorithm has also been revealed. As far as we know, this is the first work that has shown the entrywise convergence and implicit regu-larization property of a non-convex method for low Tucker-rank tensor completion. The analysis relies on the leave-one-out technique, and some of the technical results developed in the paper might be of broader interest in investigating the properties of other non-convex methods for this problem.