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[Poster] Local Convergence of the Heavy Ball method in Iterative Hard Thresholding for Low-Rank Matrix Completion

Citation Author(s):
Trung Vu, Raviv Raich
Submitted by:
Trung Vu
Last updated:
10 May 2019 - 4:00pm
Document Type:
Document Year:
Trung Vu
Paper Code:

We present a momentum-based accelerated iterative hard thresholding (IHT) for low-rank matrix completion. We analyze the convergence of the proposed Heavy Ball (HB) accelerated IHT near the solution and provide optimal step size parameters that guarantee the fastest rate of convergence. Since the optimal step sizes depend on the unknown structure of the solution matrix, we further propose a heuristic for parameter selection that is inspired by recent results in random matrix theory. Our experiment on a simple matrix completion setting verifies our analysis and illustrates the competitive rate of convergence that can be obtained with the proposed algorithm.

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