Inertial Accelerated Stochastic Mirror Descent for Large-Scale Generalized Tensor CP Decomposition

Abstract: The majority of classic tensor CP decomposition models are designed for squared loss, employing Euclidean distance as a local proximal term. However, the Euclidean distance is unsuitable for the generalized loss function applicable to various types of real-world data, such as integer and binary data. Consequently, algorithms developed under the squared loss are not easily adaptable to handle these generalized losses, partially due to the lack of the gradient Lipschitz continuity. This paper considers the generalized tensor CP decomposition. We use the Bregman distance as the proximal term and propose an inertial accelerated block randomized stochastic mirror descent algorithm (iTableSMD). Within a broader multi-block variance reduction and inertial acceleration framework, we demonstrate the sublinear convergence rate for the subsequential sequence produced by the iTableSMD algorithm. We further show that iTableSMD requires at most O({\epsilon}^{-2}) iterations in expectation to attain an {\epsilon}-stationary point and establish the global convergence of the sequence. Numerical experiments on real datasets demonstrate that our proposed algorithm is efficient and achieve better performance than the existing state-of-the-art methods.