Learning to Solve Integer Linear Programs with Davis-Yin Splitting
Abstract: In many applications, a combinatorial problem must be repeatedly solved with similar, but distinct parameters. Yet, the parameters $w$ are not directly observed; only contextual data $d$ that correlates with $w$ is available. It is tempting to use a neural network to predict $w$ given $d$. However, training such a model requires reconciling the discrete nature of combinatorial optimization with the gradient-based frameworks used to train neural networks. When the problem in question is an Integer Linear Program (ILP), one approach to overcome this training issue is to consider a continuous relaxation of the combinatorial problem. While existing methods utilizing this approach have shown to be highly effective on small problems, they do not always scale well to large problems. In this work, we draw on ideas from modern convex optimization to design a network and training scheme which scales effortlessly to problems with thousands of variables. Our experiments verify the computational advantage our proposed method enjoys on two representative problems, namely the shortest path problem and the knapsack problem.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: I'm unsure of how to provide an anonymous URL linking to the previous version, but the submission number is 2470.
The previous submission contained an non-anonymous link to a code repo, which has since been removed. On behalf of my coauthors and I, I'd like to apologize for this!
Assigned Action Editor: ~Jasper_C.H._Lee1
Submission Number: 2536
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