Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 3: Reject: For instance, a paper with technical flaws, weak evaluation, inadequate reproducibility and incompletely addressed ethical considerations.
review_content: summary: Authors propose an extension of the work A.Abbas and P.Swoboda FasdDOG, 2022. New algorithm includes graph network, which allows to learn parameters for non-parametric update and parametric step of FastDOG, 2022. 
strengths_and_weaknesses: Strengths:
1. Modification of FastDOG algorithm, which allows for:
    - graph NN for learning parameters
    - GPU parallelization 
    - non-parametric step

Weaknesses:
1. The resulting algorithm includes a non-parametric step, but there are no theoretical guarantees for the non-parametric step. 
2. Experiments part seems to be a bit unclear for me. Questions are listed in the corresponding section.
3. Experiments show that on 3 out of 4 datasets Gurobi shows better results and on two of them Gurobi does it in approximately the same time. 
4. The code is not attached. 
questions: 1. How the neural network is trained? During the optimization process, or separately? 
2. For me it is unclear, why in Table 1 training time is in hours and significantly large compared to Figure 2.
3. If training and performing optimization are separate processes, training time should be included in Figure 2. 
4. For table 2 it is also interesting to see the comparison in the number of iterations to understand the complexity of one iteration
5. Line 246. As for me, it is unfair to fix parameters in Alg. 1 for the CT dataset. It creates a fake impression of the proposed approach.
limitations: -
review_title: null

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: The authors present DOGE, a learning-based method to solve relaxations to integer programs that exploits GPU parallelism. 
Specifically, DOGE builds on a method based on Lagrangian decomposition, FastDOG, and proposes to improve its update step either by optimizing over its parameters, or by learning the update direction via a GNN.
DOGE is shown to improve on FastDOG on 4 benchmarks.
strengths_and_weaknesses: The paper is well written and easy to follow. While the results appear to be convincing on the selected benchmarks, DOGE is an incremental improvement on FastDOG, which introduced the GPU-friendly dual formulation. I believe the originality of DOGE to be limited as it only proposes to learn the update steps of FastDOG, while keeping the same formulation. Given the extent of the improvement over FastDOG over the selected benchmarks, and lack thereof in the experiments mentioned in lines 278-285, I am not sure that the cost associated to training pays off in this context.
questions: - Could the authors include the omitted negative results mentioned in lines 278-285?
limitations: The authors adequately and honestly address the limitations of their work.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper proposes a novel framework to speed up solving ILP problems through tuning parameters of Parallel Deferred Min-Marginal Averaging algorithm. This tuning is based on the gradients of the loss function w.r.t to these parameters, so the ILP solver is represented as a neural network that can be optimized with gradient-based optimization method. The los function here is explicit dual objective function. The parameters update preserves their feasibility and non-decrease of the lower-bound. Moreover, to prevent stuck in fixed point, non-parametric update step is also proposed and separate model to generate it is trained. The presented method is evaluated in four classes of combinatorial problems, shows faster convergence than Gurobi solver and establishes smaller relative duality gap.
strengths_and_weaknesses: Strengths:
1) extensive computational experiments for evaluation of the proposed method
2) the novel technique for differentiating optimization methods w.r.t. its parameters
3) recipes how to escape from the fixed points
4) unsupervised loss function eliminates any data preparation stage

Weaknesses:
1) hand-crafted features for GNN requires some approach to encode current state of Alg 1 in automatic way or some theory that explains the sufficiency of the presented set of features
2) it remains unclear why such complicated procedure that computes gradients, updates parameters of optimizer in two-ways (parametric and non-parametric) and requires additional memory to store parameters of neural networks is still faster than the state-of-the-art solvers like Gurobi.  
questions: Please comment the following remarks and questions:
1) In line 34, authors claim that simplex or interior-point methods are not GPU friendly, however, they consist of series of linear algebra operations, that can be speed up due to GPU architectures e.g. matrix multiplication in dense layers of neural networks is faster on GPU rather than on CPU. Please, provide more detailed explanation of this point. 
2) What is the motivation for forward and backward iterations over blocks $B_1,\ldots, B_u$ in algorithm 1?
3) Please provide more details about computing subgradients in eq 23 from Appendix. Since this is the single non-trivial operation in the differentiating of the considered method (others operations are just summation and subtraction), its detailed description is important for understanding the correctness of the proposed approach.
4) Alg 2 solves two optimization problems (for $\beta = 0$ and $\beta = 1$), so it is not clear the difference with the naive implementation. Please, provide more details or explicitly present the naive form and highlight the difference.
5) Please provide detailed description of datasets that are used in generating of Figure 2. Do these plots correspond to a picked instance of the corresponding problem class? Or some average over all considered instances are made? 
6) What solver do authors use inside the proposed framework to solve problems in line 10, Alg 1 and in line 4, Alg 2?
7) Please explicitly describe how to transform standard constraints like $Ax \leq b$ to the form in problem (BP) ?
8) Please explicitly state and describe decreasing of what quantities can explain the observed speed up. Are they the overall number of iterations, acceleration of solving intermediate optimization problems with GPU, or anything else? Such comparison with other state-of-the-art methods helps to place the proposed framework in the proper context and improve understanding of the reasons for the observed gain. If such comparison is not possible for Gurobi since authors do not have access to its detailed statistics, it is possible for FastDog, which is non-differentiable version of the proposed approach with fixed parameters $\omega_{ij}$ and $\alpha_{ij}$.
9) I assume that in line 123 $\omega$ should be replaced with $\omega_{ij}$ according to the line 10 in Alg. 1 
limitations: The authors explicitly state the problems where the proposed framework does not show improvement and discuss the possible reasons for that.
review_title: null

Meta-review: metareview: The presented paper introduces DOGE-Train method that targets discrete optimization problems. It allows finding solutions for discrete problems utilizing GPUs. This is achieved by pre-training on smaller size instances and then hoping it would also generalize for larger instances that are coming from a similar family of problems. Overall, the idea is related to FastDOG but has some improvements.

Despite showing promising results, there are still a few concerns raised by reviewer "ehgi". Also, I am not sure if the NeurIPS would be the best fit for this paper.


confidence: Less certain
Decision: Reject