Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: This paper seeks to apply the techniques developed for adversarial robustness in machine learning to the problem of robust optimal power flow. It presents a formulation for the robust optimization problem, shows an efficient gradient-based optimization method and evaluates the effectiveness of the method.
main_review: I have to admit that this paper is a little outside of my expertise. My experience is mostly in adversarial robustness in machine learning. This work is more about optimal power flow. The paper does not seem to have any connection to adversarial learning apart from the fact that it uses adversarial training to robustly optimize an objective function. Having said that, I find this to be an interesting paper that utilizes the techniques used in adversarial robustness to design robust solutions for the optimal power flow problem. The paper combines well-known mathematical concepts, such as implicit function theorem and implicit differentiation, in a new way to achieve this goal. The method developed in this work is clearly presented and is backed up with theoretical analysis and experimental evaluation. It might also have applications other than the problem of optimal power flow considered in this paper.
limitations_and_societal_impact: The authors have discussed the limitations and societal impact of the work.
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: This paper formulates a challenging optimal power flow problem as adversarial optimization problem, where the adversarial optimization problem has a challenging equality constraint.  The paper gives a principled approach to solve this problem and give convincing empirical results of the superiority of the approach.
main_review: It is delightful read. The paper is very crisp: problem definitions, approach, derivations, etc. And empirical results demonstrate convincingly its effectiveness, especially for N-2, and N-3 settings.

I am however not familiar with optimal power flow problem -- Is it really important to solve N-2 and N-3 settings? More discussions would be useful.
limitations_and_societal_impact: Yes
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: In this paper, N-k SCOPF is formulated and solved through the lens of adversarial learning and the implicit function theory. Thus, problem formulation and the development of a multi-level optimization algorithm are two key contributions. Meanwhile, the paper is mostly well written and easy to follow. 
main_review: Strength:

+ Rewriting N-k SCOPF as a minimax problem is a novel idea. 

+ Obtaining (implicit) attack gradients via KKT conditions is interesting. 

+ The proposed seems scalable even if high-order derivatives and matrix inversion exist. 

Weakness:

- Although the paper is written well in general, several important details are missing in the main paper. For example, Appendix B should be placed in the main body since this is a critical derivation to obtain implicit gradients. Moreover, a pseudo-algorithm that summarizes both attacks and defend steps will make the proposed optimization steps clear. 

- In Eq. (11), it is not clear how to simplify the computation of $J^{-1}$.  Also, will $\frac{d J}{d y}$ involve higher-order derivatives? If so, how to overcome the scalability issue?

- A computation complexity analysis of the proposed algorithm, e..g, in the big O notation, will make the scalability argument more convincing. 

- The implementation details of the proposed algorithm were not clearly discussed in experiments. E.g., hyper-parameter selection associated with the algorithm?

limitations_and_societal_impact: Yes, the authors have adequately discussed the limitations and potential negative societal impact.
review_title: null

final_score: rating: 8: Top 50% of accepted NeurIPS papers, clear accept
review_content: summary: The authors develop a new method for solving the N-k SCOPF problem, an optimal power flow problem robust to any $k$ outages. Specifically, they relax the problem to allow for any convex combination of outages that has total 1-norm less than $k$. They then leverage recently popularized implicit differentiation techniques to solve the resulting minimax problem. Their formulation works for generic minimax problems, although one can exploit problem-specific structure when solving the N-k SCOPF problem. Finally, they test their method on a reasonably large test case for $k = 1, 2, 3$, and show that it finds a solution in a reasonable amount of time that improves upon standard OPF (in terms of the number of violations).
main_review: The main contribution of the paper is to use implicit differentiation to solve a relaxed version of the N-k SCOPF problem. This contribution is novel (as far as I’m aware of) and clearly addresses the scalability issues that arise when solving robust OPF problems on large networks. Given the large size of most real power networks, the paper represents an important step towards scaling N-k OPF to real networks (for $k >= 2$ of course).

The results appear technically sound, and the writing is very clear. One statement I found slightly confusing was that on line 223—why wouldn’t projected gradient descent guarantee feasibility (shouldn’t the projection onto the feasible set take care of this)?

The experiments section clearly verified that the method works and produces reasonable results in an acceptable amount of time. However, I’m not 100% certain this method produces better results than a simple robust OPF solver (how does it compare to N-1 SCOPF), since comparing directly to standard OPF is a bit of a straw man. Would it be possible to add the number of violations produced by N-1 SCOPF to Table 2? This would give the reader a better sense of how this method compares to standard robust OPF methods (especially since N-1 is so often used in practice).



Minor Comments
- On line 95, should maximizer and minimizer be switched? 
- What is the origin / purpose / utility of the name CAN$\partial$Y?
- In Table 1, is a lower or higher score better?
limitations_and_societal_impact: Although the author allude to the lack of theoretical guarantees associated with their method in the first paragraph of the introduction, it would be nice to state this limitation explicitly later in the paper.

The broader impact, including the potential negative societal impact, are clearly stated in the paper.
review_title: null

Meta-review: This paper considers the N-k security-constrained optimal power flow problem using ideas from adversarially robust training. In particular, they design gradient based methods to solve this problem and implement it on N-3 SCOPF which has been traditionally considered out of reach of existing approaches. All the reviewers agree that this paper makes a nice and interesting contribution to this problem and recommend acceptance.
Decision: Accept (Poster)