This paper studies how to design abstractions of large-scale combinatorial optimization problems that can leverage existing state-of-the-art solvers in general-purpose ways, and that are amenable to data-driven design. The goal is to arrive at new approaches that can reliably outperform existing solvers in wall-clock time. We focus on solving integer programs and ground our approach in the large neighborhood search (LNS) paradigm, which iteratively chooses a subset of variables to optimize while leaving the remainder fixed. The appeal of LNS is that it can easily use any existing solver as a subroutine, and thus can inherit the benefits of carefully engineered heuristic approaches and their software implementations. We also show that one can learn a good neighborhood selector from training data. Through an extensive empirical validation, we demonstrate that our LNS framework can significantly outperform, in wall-clock time, compared to state-of-the-art commercial solvers such as Gurobi.

This paper studies a strategy for data-driven algorithm design for large-scale combinatorial optimization problems that can leverage existing state-of-the-art solvers in general purpose ways. The goal is to arrive at new approaches that can reliably outperform existing solvers in wall-clock time. We focus on solving integer linear programs, and ground our approach in the large neighborhood search (LNS) paradigm, which iteratively chooses a subset of variables to optimize while leaving the remainder fixed. The appeal of LNS is that it can easily use any existing solver as a subroutine, and thus can inherit the benefits of carefully engineered heuristic or complete approaches and their software implementations. We show that one can learn a good neighborhood selector using imitation and reinforcement learning techniques. Through an extensive empirical validation in bounded-time optimization, we demonstrate that our LNS framework can significantly outperform compared to state-of-the-art commercial solvers such as Gurobi.

Additional Feedback: I wonder whether the used LNS requires a local search algorithm for solving the subproblem (Line 3). The authors argue that they set \gamma to 1 because it is a finite-horizon task. I completely agree that this is a possible choice; however even for finite-horizon tasks, \gamma can be set to values smaller than 1.0. I wonder how sensitive their approach is to such hyperparameters. The authors sampled 5 trajectories for each problem (instance?) to estimate the policy gradient. I'm not sure whether I understood that point fully.

This paper received positive reviews from all three reviewers but during the discussion there was widespread concern about whether the contribution is of sufficient significance for a NeurIPS publication. In particular, the question was raised whether a paper that merely applies ML techniques in a new application domain was of sufficient significance. I also read the paper and the author's rebuttal and I very much agree with the authors on this point: application papers have always been a part of the major ML conferences and can help drive the field forward. I am therefore happy to recommend acceptance and encourage the authors to spend more text in the final version towards motivating the problem to a general audience.

This paper studies how to design abstractions of large-scale combinatorial optimization problems that can leverage existing state-of-the-art solvers in general-purpose ways, and that are amenable to data-driven design. The goal is to arrive at new approaches that can reliably outperform existing solvers in wall-clock time. We focus on solving integer programs and ground our approach in the large neighborhood search (LNS) paradigm, which iteratively chooses a subset of variables to optimize while leaving the remainder fixed. The appeal of LNS is that it can easily use any existing solver as a subroutine, and thus can inherit the benefits of carefully engineered heuristic approaches and their software implementations. We also show that one can learn a good neighborhood selector from training data.