NeurIPS 2019
Sun Dec 8th through Sat the 14th, 2019 at Vancouver Convention Center

### Reviewer 1

I've read the response and the justification for assumptions A and B are nice. The score has increased to 7. ---------------------------------------------------------------------- 1. Originality: This paper devises a new distance function applied in BGP algorithm. The framework is existing but the author gives a number of improvements and for the first time gives convergence theorem under some conditions. 2. Quality: The theoretical derivation looks sound and the experiments are rather comprehensive. 3. Clarity: The text is mainly clear, but the statement of BPG-MF algorithm is a little confusing --- one needs to read through many sections to get the whole algorithm. 4. Significance: The results are theoretically valuable as a non-alternating optimization method with thorough analysis. But in real data experiments this algorithm does not show a significant advantage in performance over the traditional methods, especially when computing resource is limited.

### Reviewer 2

In this study, inertial Bregman proximal gradient algorithms (BPG and CoCaIn-BPG) were considered for matrix factorization. The problem here was the existence of L-smad property in matrix factorization. To tackle this issue, Authors proposed a novel Bregman distance, and proved the L-smad property with this distance and infer convergence of BPG and CoCaIn BPG. I think the contributions in this paper is novel and significant. In experiments, three problems (matrix factorization, non-negative matrix factorization, and matrix completion) were solved by the proposed optimization algorithms and the effectiveness compared with state-of-the-art algorithms such as PALM, iPALM was demonstrated. I think it was nice if the convergence behaviors are statistically evaluated because the stationary points obtained by non-convex optimization are usually varied by initialization. Thus, I claim that the experiments are slightly weak.
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