Optimistic Acceleration for Optimization
We consider new variants of optimization algorithms. Our algorithms are based on the observation that mini-batch of stochastic gradients in consecutive iterations do not change drastically and consequently may be predictable. Inspired by the similar setting in online learning literature called Optimistic Online learning, we propose two new optimistic algorithms for AMSGrad and Adam, respectively, by exploiting the predictability of gradients. The new algorithms combine the idea of momentum method, adaptive gradient method, and algorithms in Optimistic Online learning, which leads to speed up in training deep neural nets in practice.
 In this manuscript, the authors borrow the idea of "optimism" from the online learning literature and apply it to two frequently used methods for neural network training (AMSGrad and ADAM). More or less, replicating the theory known in the literature, they give a regret analysis. The manuscript ends with a comparison of the optimistic methods against their plain counterparts on a set of test problems. This is a well-written paper filling a gap in the literature. Through the contribution does not seem significant, the results do support that such extensions should be out there. In addition to a few typos, some clarification on several points could be quite useful: 1) It is not clear why the authors use this particular extrapolation algorithm? 2) If we have the past r+1 gradients, can we put them into use for scaling the next direction like in quasi-Newton methods? 3) The following part of the sentence is not clear: "... the gradient vectors at a specific time span is assumed to be captured by (5)." 4) .nabla is missing at the end of the line right after equation (6). 5) The second line after Lemma 2 should be "... it does not matter how..." (The word *not* is missing.)
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Optimistic Acceleration for Optimization
We consider new variants of optimization algorithms. Our algorithms are based on the observation that mini-batch of stochastic gradients in consecutive iterations do not change drastically and consequently may be predictable. Inspired by the similar setting in online learning literature called Optimistic Online learning, we propose two new optimistic algorithms for AMSGrad and Adam, respectively, by exploiting the predictability of gradients. The new algorithms combine the idea of momentum method, adaptive gradient method, and algorithms in Optimistic Online learning, which leads to speed up in training deep neural nets in practice.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 In this manuscript, the authors borrow the idea of "optimism" from the online learning literature and apply it to two frequently used methods for neural network training (AMSGrad and ADAM). More or less, replicating the theory known in the literature, they give a regret analysis. The manuscript ends with a comparison of the optimistic methods against their plain counterparts on a set of test problems. This is a well-written paper filling a gap in the literature. Through the contribution does not seem significant, the results do support that such extensions should be out there. In addition to a few typos, some clarification on several points could be quite useful: 1) It is not clear why the authors use this particular extrapolation algorithm? 2) If we have the past r+1 gradients, can we put them into use for scaling the next direction like in quasi-Newton methods? 3) The following part of the sentence is not clear: "... the gradient vectors at a specific time span is assumed to be captured by (5)." 4) .nabla is missing at the end of the line right after equation (6). 5) The second line after Lemma 2 should be "... it does not matter how..." (The word *not* is missing.)
assistant
 In this manuscript, the authors borrow the idea of "optimism" from the online learning literature and apply it to two frequently used methods for neural network training (AMSGrad and ADAM). More or less, replicating the theory known in the literature, they give a regret analysis. The manuscript ends with a comparison of the optimistic methods against their plain counterparts on a set of test problems. This is a well-written paper filling a gap in the literature. Through the contribution does not seem significant, the results do support that such extensions should be out there. In addition to a few typos, some clarification on several points could be quite useful: 1) It is not clear why the authors use this particular extrapolation algorithm? 2) If we have the past r+1 gradients, can we put them into use for scaling the next direction like in quasi-Newton methods? 3) The following part of the sentence is not clear: "... the gradient vectors at a specific time span is assumed to be captured by (5)." 4) .nabla is missing at the end of the line right after equation (6). 5) The second line after Lemma 2 should be "... it does not matter how..." (The word *not* is missing.)