Doubly Accelerated Proximal Gradient for Nonnegative Tensor Decomposition

The accelerated proximal gradient (APG) is a classical algorithm for nonnegative tensor decomposition. The APG employs variable extrapolation to accelerate the computation. However, large-scale tensor decomposition still requires more efficient algorithms. In this paper, we propose a doubly accelerated proximal gradient algorithm. Specifically, in the block coordinate descent framework, we utilize double extrapolations in both the inner and outer loops to accelerate the proximal gradient. Moreover, a safe mode comes with the acceleration in the outer loop to enhance monotonic convergence. We conduct experiments on both synthetic and real-world tensors. The results demonstrate that the proposed algorithm outperforms state-of-the-art algorithms in running speed and accuracy.