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In many applications, a combinatorial problem must be repeatedly solved withsimilar, but distinct parameters. Yet, the parameters $w$ are not directlyobserved; only contextual data $d$ that correlates with $w$ is available. It istempting to use a neural network to predict $w$ given $d$, but training such amodel requires reconciling the discrete nature of combinatorial optimizationwith the gradient-based frameworks used to train neural networks. When theproblem in question is an Integer Linear Program (ILP), one approach toovercoming this issue is to consider a continuous relaxation of thecombinatorial problem. While existing methods utilizing this approach haveshown to be highly effective on small problems (10-100 variables), they do notscale well to large problems. In this work, we draw on ideas from modern convexoptimization to design a network and training scheme which scales effortlesslyto problems with thousands of variables.

Faster Predict-and-Optimize with Davis-Yin Splitting