Deep Unfolded Multicast Beamforming

Takabe, Satoshi; Wadayama, Tadashi

doi:10.48550/arxiv.2004.09345

Cited by 1 publication

(1 citation statement)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, numerous studies on signal processing algorithms focusing deep unfolding have been presented for sparse signal recovery [3]- [8], image recovery [9]- [12], wireless communications [13]- [19], and distributed computing [20]. Theoretical aspects of deep unfolding have also been investigated [21]- [23], which mainly focus on analyses of deep-unfolded sparse signal recovery algorithms.…”

Section: Introductionmentioning

confidence: 99%

Convergence Acceleration via Chebyshev Step: Plausible Interpretation of Deep-Unfolded Gradient Descent

Takabe¹,

Wadayama²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

Deep unfolding is a promising deep-learning technique, whose network architecture is based on expanding the recursive structure of existing iterative algorithms. Although convergence acceleration is a remarkable advantage of deep unfolding, its theoretical aspects have not been revealed yet. The first half of this study details the theoretical analysis of the convergence acceleration in deep-unfolded gradient descent (DUGD) whose trainable parameters are step sizes. We propose a plausible interpretation of the learned step-size parameters in DUGD by introducing the principle of Chebyshev steps derived from Chebyshev polynomials. The use of Chebyshev steps in gradient descent (GD) enables us to bound the spectral radius of a matrix governing the convergence speed of GD, leading to a tight upper bound on the convergence rate. The convergence rate of GD using Chebyshev steps is shown to be asymptotically optimal, although it has no momentum terms. We also show that Chebyshev steps numerically explain the learned step-size parameters in DUGD well. In the second half of the study, Chebyshev-periodical successive over-relaxation (Chebyshev-PSOR) is proposed for accelerating linear/nonlinear fixed-point iterations. Theoretical analysis and numerical experiments indicate that Chebyshev-PSOR exhibits significantly faster convergence for various examples such as Jacobi method and proximal gradient methods.

show abstract