__ Summary and Contributions__: This work studies learning under Massart noise, following up on the recent
breakthrough algorithm for learning halfspaces by Diakonikolas et al. In this
work, a vastly simpler proper halfspace learning algorithm is proposed, as well
as algorithms for learning generalized linear models under Massart noise.
These algorithms can only guarantee accuracy up to the (maximum) noise rate.
This work also presents a connection between learning under Massart noise and
(correlational) statistical query algorithms/evolvability, and shows that no
distribution-independent algorithm that makes only a polynomial number of
queries can match the error rate of the optimal halfspace (which may be lower
than the noise rate).
Finally, some experiments are presented, demonstrating that different
(Massart-style) noise rates on different populations can lead standard
classifiers to produce different error rates across populations, but that the
algorithm presented here (along with the uninterpretable random forest) is
resilient to this effect.

__ Strengths__: This is a bundle of several results, each of which are pretty interesting in
their own right. The main algorithm for learning halfspaces is a pretty strong
result. It is vastly simpler than the Diakonikolas et al. algorithm, provides a
single halfspace as a hypothesis, and actually evades a negative result of
Diakonikolas et al. showing that minimizing a fixed surrogate loss cannot
succeed. The extension to GLMs and the connection to CSQ/evolvability, used to
obtain the lower bound for matching OPT (< noise rate), are indeed also quite
nice. Finally, the discussion of the connection to algorithmic fairness is
interesting.

__ Weaknesses__: My only complaint is that the connection to fairness could have been
investigated a little more thoroughly. A single effect resulting from explicit
Massart-like noise is presented in the experiments, but the introduction
suggests some broader motivation -- I am assuming that the suggestion is that
the misreporting should be viewed as Massart noise, but I am not sure if the
misreporting due to, e.g., low levels of trust should be viewed as Massart-style
noise. Likewise, in the strategic classification example, I am not sure if
Massart-style noise is a good model. I would think that to support these kinds
of claims, you should demonstrate that the Massart-resilient learner achieves
for example, more consistent accuracy across groups in the kinds of data where
these effects have been demonstrated. It is an intriguing suggestion, but
somewhat underdeveloped here.

__ Correctness__: The body of the paper is somewhat scant on details. A claim about distillation
of improper hypotheses to proper hypotheses is made in the introduction and not
discussed in any further detail in the body of the paper. It's hard to judge the
correctness of most of the work based on what's written in the body; it's
plausible but not truly convincing. I recognize that the proofs do appear in
the supplemental material, and I recognize that the page limit does not permit
the authors to present the work as they'd wish. Still, I would hope for more
discussion of what enables the main claims to be obtained.

__ Clarity__: Some parts of the paper are very well written and some parts are rough. I
appreciated the overview of the proper halfspace learning algorithm and the
connection to the CSQ model. The section on learning GLMs gives a fair overview,
but it's a bit too high level and vague at times, to take much away (continuing
my complaint above). Likewise, the discussion of fairness could have benefitted
from a more careful discussion of how exactly Massart-resilient learning
protects against the effect described at the top of p.8.
I think this paper would have benefitted from giving a more thorough
presentation of more limited claims, perhaps even from being split into two. The
results seem strong enough to have supported more than one submission.

__ Relation to Prior Work__: Yes.

__ Reproducibility__: Yes

__ Additional Feedback__: Update post-response: I cannot envision a world in which this paper is rejected on the basis of my relatively low score of 7. But, I really do believe that this should have been split in two companion papers, perhaps with the text of the first paper included in the supplemental material of the second. It does not matter that the algorithm for GLMs shares ideas with the proper learning algorithm; obviously, one often builds upon the ideas of other, prior works. I stress again, it's hard to get much out of the presentation here, to the point that the paper is more "planting a flag" on the result than communicating the ideas involved.

__ Summary and Contributions__: The paper extends the recent work of Diakonikolas et al on learning halfspaces with Massart noise. In particular the authors provide an algorithm that properly learns halfspaces under Massart noise. Furthermore, they provide an efficient algorithm for generalized linear models under a noise model that yields Massart noise as a special case. The authors also provide a super-polynomial lower bound on the number of queries needed for learning halfspaces distribution-independently under Massart noise. Finally, the authors evaluate empirically their work on the UCI Adult dataset.

__ Strengths__: This seems to be a very interesting paper with connections to different topics in learning theory, including evolvability and fairness. The algorithms for learning halfspaces, as well as learning generalized linear models are the main contributions of the paper. The paper is relevant to the NeurIPS community (though it appears to be a more computational learning theory type of paper), and there is an extensive appendix (which I must admit I only skimmed through some claims and proofs) that defines the different topics and provides the details to the various claims.

__ Weaknesses__: The only weakness that I can think of is the fact that learning halfspaces under Massart noise has already been done by Diakonikolas et al. last year -- though improperly. Here the contribution is that learning halfspace can be done properly. Of course, in the course of providing this proper learning result the authors also shed light to issues and questions that remained open from the work of Diakonikolas et al; therefore, in the end, the whole approach is definitely worth it.

__ Correctness__: There is an extensive appendix with the claims and the proofs. I skimmed through several of them and it appears to be ok. Similarly, the empirical methodology appears to be correct.

__ Clarity__: The paper is well-written and this appears to be the case in the appendix, to the extent that I read some parts. I only have a few remarks.
Line 19: "hypothesis" --> ground truth function
Lines 39-42: The Massart noise model was known/used earlier. I think the correct reference is Robert Sloan's paper "Four types of noise in data for PAC learning" where the noise model was introduced and is called as the "malicious misclassification noise model" there.
Line 155: D is defined to be the distribution in line 169. This should be done here as well.

__ Relation to Prior Work__: Yes, the paper positions well its results with respect to the related work.

__ Reproducibility__: Yes

__ Additional Feedback__: After rebuttal: Thank you for a very interesting paper.

__ Summary and Contributions__: This makes the recent breakthrough results on learning halfspaces proper and also gives an SQ lower bound for getting OPT + \epsilon.

__ Strengths__: Clearly a great result. A very important improvement on recent work due to Diakonikolas et al. Well written. Several clever ideas and an interesting tie-in to evolvability.

__ Weaknesses__: None

__ Correctness__: Yes

__ Clarity__: Yes

__ Relation to Prior Work__: Yes

__ Reproducibility__: Yes

__ Additional Feedback__: A must accept.

__ Summary and Contributions__: The paper extends results on learnability with Massart noise.
While previous work settled the open question of learnability of halfspaces by showing an improper learner exists, this work provides a proper learner.
Another extension this work offers is to the class of Generalized Linear Models, where an improper learner for GLMs under Massart noise is given.
Finally, a lower bound is given for the number of Correlation Statistical Queries required for learning halfspaces under Massart noise, using a nice connection to previous work on Correlational Statistical Queries.

__ Strengths__: The paper provides insights into interesting questions that are relevant to the learning theory community, and are receiving increased attention following the developments in last year's paper about learning with Massart noise.
Technically, the proofs seem to contain several novel developments over the work of Diakonikolas et al. The results on GLMs and connections to Statistical Queries are also novel and significant.
Although I am not highly knowledgable on these specific aspects of learning theory, the paper looks like a solid contribution to me.

__ Weaknesses__: I did not find very clear weaknesses with the paper, although I do think it may be possible to discuss the connection between its different parts in more detail.
For instance, It would be nice to give a few words about why the knowledge distillation approach from the paper is inapplicable to get a proper learner for GLMs. Or more broadly, are there any technical insights that the analysis in the paper gives towards resolving the question of proper learning in GLMs?
In my humble opinion, a small table summing up the known bounds under the different settings, or a discussion at the end of the paper, can also be helpful for readers who want to get an overview of the results and open issues.

__ Correctness__: The claims are correct and backed up by rigorous proofs.

__ Clarity__: For a paper that is rich in technical details, the paper is not hard to read.
As pointed out earlier, I think that it could be useful to have a condensed overview of the results and the conclusions.

__ Relation to Prior Work__: Relation to prior work is discussed adequately.

__ Reproducibility__: Yes

__ Additional Feedback__: Small comments:
1) Equation numberings and hyperlinks seem to be malfunctioning (e.g. I couldn't find any of the numberings on the equations).
2) In line 131 it is stated that \sigma=0 is essentially the same as agnostic learning. While I can see why this makes sense, it doesn't look like an entirely trivial statement (unless I am missing something here). It might be good to consider adding a short comment about that.