[mcintyre1994]

Can you use the typical approaches to classification? You can define a continuous error function and perform back-propagation using that. If you look at something like Kaggle then deep learning approaches tend to dominate classification challenges just as much as they do regression ones.

[bitL]

That's the usual approach which has its limits. I am specifically curious about discrete domains. Look at it as at mixed integer programming - yes, you can estimate solution using linear programming, but that estimate is usually useless. Having a specific method for mixed integer programming usually yields far better solutions.