StoTAM: Stochastic Alternating Minimization for Tucker-Structured Tensor Sensing
Shuang Li
TL;DR
StoTAM tackles low-Tucker-rank tensor sensing from linear measurements by optimizing over the Tucker core and factor matrices in a stochastic alternating-minimization framework. The core tensor is updated via a closed-form mini-batch least-squares solution, while each factor matrix is updated on the Stiefel manifold using mini-batch stochastic gradients and QR retractions, avoiding costly tensor projections. Compared to StoTIHT, StoTAM significantly reduces memory and computational demands and demonstrates faster wall-clock convergence on synthetic data. This approach enhances scalability for large-scale tensor recovery and broadens the applicability of stochastic optimization to Tucker-structured models.
Abstract
Low-rank tensor sensing is a fundamental problem with broad applications in signal processing and machine learning. Among various tensor models, low-Tucker-rank tensors are particularly attractive for capturing multi-mode subspace structures in high-dimensional data. Existing recovery methods either operate on the full tensor variable with expensive tensor projections, or adopt factorized formulations that still rely on full-gradient computations, while most stochastic factorized approaches are restricted to tensor decomposition settings. In this work, we propose a stochastic alternating minimization algorithm that operates directly on the core tensor and factor matrices under a Tucker factorization. The proposed method avoids repeated tensor projections and enables efficient mini-batch updates on low-dimensional tensor factors. Numerical experiments on synthetic tensor sensing demonstrate that the proposed algorithm exhibits favorable convergence behavior in wall-clock time compared with representative stochastic tensor recovery baselines.