Improved Gradient Estimators for Stochastic Discrete Variables
In many applications we seek to optimize an expectation with respect to a distribution over discrete variables. Estimating gradients of such objectives with respect to the distribution parameters is a challenging problem. We analyze existing solutions including finite-difference (FD) estimators and continuous relaxation (CR) estimators in terms of bias and variance. We show that the commonly used Gumbel-Softmax estimator is biased and propose a simple method to reduce it. We also derive a simpler piece-wise linear continuous relaxation that also possesses reduced bias. We demonstrate empirically that reduced bias leads to a better performance in variational inference and on binary optimization tasks.
 After revision: The authors have addressed all points in my review. Although I will not be increasing the score, these fixes certainly increase the confidence of my evaluation and I think it deserves to be accepted. ==================== Summary: This paper analyzes finite-difference and continuous relaxation gradient estimators for discrete random variables and from their analysis develop improvements to these existing methods. They empirically demonstrate the improvement by evaluating the gradient estimators on toy tasks and an autoencoding task. Writing: I found this paper very well written and explained. It covered an extensive background concisely while introducing all necessary ideas to understand the contributions of the paper. Comments: Overall, I found the ideas presented in this paper interesting and novel, and results sufficiently strong to support the ideas. Though the contributions are not groundbreaking, they will certainly be useful to researchers in this space. I have some minor comments relating to notation and related work. - I found the notation in Section 3.2 to be a little confusing, namely that appears as both a random variable and a continuous function (that takes in one variable in the paragraph after eq11, but takes in two variables in eq15). I understand that the authors may have done this to suppress extra notation, but I found this section harder to understand than the rest due to this choice. There is also a small typo in eq2 where the from is dropped. - I think it would be useful to compare IGSM and PWL against a score-function gradient estimator (maybe REBAR, given the similarity in experiment setup). The authors do contextualize the line of work concerning score-function gradient estimators. However, since SF estimators are unbiased but high variance and the authors aim to reduce bias at the cost of variance, I think evaluating SF baselines will better contextualize the tradeoffs made in this paper.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Improved Gradient Estimators for Stochastic Discrete Variables
In many applications we seek to optimize an expectation with respect to a distribution over discrete variables. Estimating gradients of such objectives with respect to the distribution parameters is a challenging problem. We analyze existing solutions including finite-difference (FD) estimators and continuous relaxation (CR) estimators in terms of bias and variance. We show that the commonly used Gumbel-Softmax estimator is biased and propose a simple method to reduce it. We also derive a simpler piece-wise linear continuous relaxation that also possesses reduced bias. We demonstrate empirically that reduced bias leads to a better performance in variational inference and on binary optimization tasks.
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>



 After revision: The authors have addressed all points in my review. Although I will not be increasing the score, these fixes certainly increase the confidence of my evaluation and I think it deserves to be accepted. ==================== Summary: This paper analyzes finite-difference and continuous relaxation gradient estimators for discrete random variables and from their analysis develop improvements to these existing methods. They empirically demonstrate the improvement by evaluating the gradient estimators on toy tasks and an autoencoding task. Writing: I found this paper very well written and explained. It covered an extensive background concisely while introducing all necessary ideas to understand the contributions of the paper. Comments: Overall, I found the ideas presented in this paper interesting and novel, and results sufficiently strong to support the ideas. Though the contributions are not groundbreaking, they will certainly be useful to researchers in this space. I have some minor comments relating to notation and related work. - I found the notation in Section 3.2 to be a little confusing, namely that appears as both a random variable and a continuous function (that takes in one variable in the paragraph after eq11, but takes in two variables in eq15). I understand that the authors may have done this to suppress extra notation, but I found this section harder to understand than the rest due to this choice. There is also a small typo in eq2 where the from is dropped. - I think it would be useful to compare IGSM and PWL against a score-function gradient estimator (maybe REBAR, given the similarity in experiment setup). The authors do contextualize the line of work concerning score-function gradient estimators. However, since SF estimators are unbiased but high variance and the authors aim to reduce bias at the cost of variance, I think evaluating SF baselines will better contextualize the tradeoffs made in this paper.
assistant
 After revision: The authors have addressed all points in my review. Although I will not be increasing the score, these fixes certainly increase the confidence of my evaluation and I think it deserves to be accepted. ==================== Summary: This paper analyzes finite-difference and continuous relaxation gradient estimators for discrete random variables and from their analysis develop improvements to these existing methods. They empirically demonstrate the improvement by evaluating the gradient estimators on toy tasks and an autoencoding task. Writing: I found this paper very well written and explained. It covered an extensive background concisely while introducing all necessary ideas to understand the contributions of the paper. Comments: Overall, I found the ideas presented in this paper interesting and novel, and results sufficiently strong to support the ideas. Though the contributions are not groundbreaking, they will certainly be useful to researchers in this space. I have some minor comments relating to notation and related work. - I found the notation in Section 3.2 to be a little confusing, namely that appears as both a random variable and a continuous function (that takes in one variable in the paragraph after eq11, but takes in two variables in eq15). I understand that the authors may have done this to suppress extra notation, but I found this section harder to understand than the rest due to this choice. There is also a small typo in eq2 where the from is dropped. - I think it would be useful to compare IGSM and PWL against a score-function gradient estimator (maybe REBAR, given the similarity in experiment setup). The authors do contextualize the line of work concerning score-function gradient estimators. However, since SF estimators are unbiased but high variance and the authors aim to reduce bias at the cost of variance, I think evaluating SF baselines will better contextualize the tradeoffs made in this paper.