Paper:
Hyperparameter tuning is one of the most time-consuming workloads in deep learning. State-of-the-art optimizers, such as AdaGrad, RMSProp and Adam, reduce this labor by adaptively tuning an individual learning rate for each variable. Recently researchers have shown renewed interest in simpler methods like momentum SGD as they may yield better results. Motivated by this trend, we ask: can simple adaptive methods, based on SGD perform as well or better? We revisit the momentum SGD algorithm and show that hand-tuning a single learning rate and momentum makes it competitive with Adam. We then analyze its robustness to learning rate misspecification and objective curvature variation. Based on these insights, we design YELLOWFIN, an automatic tuner for momentum and learning rate in SGD. YELLOWFIN optionally uses a negative-feedback loop to compensate for the momentum dynamics in asynchronous settings on the fly. We empirically show YELLOWFIN can converge in fewer iterations than Adam on ResNets and LSTMs for image recognition, language modeling and constituency parsing, with a speedup of up to 3.28x in synchronous and up to 2.69x in asynchronous settings.

Review:
This paper proposes a method to automatically tuning the momentum parameter in momentum SGD methods, which achieves better results and fast convergence speed than state-of-the-art Adam algorithm.
Although the results are promising, I found the presentation of this paper almost inaccessible to me.
First, though a minor point, but where does the name *YellowFin* come from?
For the presentation, the motivation in introduction is fine, but the following section about momentum operator is hard to follow. There are a lot of undefined notation. For example, what does the *convergence rate* mean (what is the measurement for convergence)? And is the *optimal accelerated rate* the same as *convergence rate* mentioned above? Also, what do you mean by *all directions* in the sentence below eq.2?
Then the paper talks about robustness properties of the momentum operator. But: first, I am not sure why the derivative of f(x) is defined as in eq.3, how is that related to the original definition of derivative?
In the following paragraph, what is *contraction*? Does it have anything to do with the paper as I didn't see it in the remaining text?
Lemma 2 seems to use the spectral radius of the momentum operator as the *robustness*. But how can it describe the robustness? More details are needed to understand this.
What it comes to Section 3, it seems to me that the authors try to use a local quadratic approximation for the original function f(x), and use the results in last section to find the optimal momentum parameter. I got confused in this section because eq.9 defines f(x) as a quadratic function. Is this f(x) the original function (non quadratic) or just the local quadratic approximation? If it is the local quadratic approximation, how is it correlated to the original function? It seems to me that the authors try to say if h and C are calculated from the original function, then this f(x) is a local quadratic approximation? If what I think is correct, I think it would be important to show this.
Also, the objective function in SingleStep algorithm seems to come from eq.13, but I failed to get the exact reasoning.
Overall, I think this is an interesting paper, but the presentation is too fuzzy to get it evaluated.