Active learning for inferring a convex optimization formulation
Those are some very technical terms to be throwing around and although I'm familiar with some of the literature from either side, I don't think that I've ever seen them used together. What is the distinction between using a convex program and an LP? They are significantly different, and you refer to both in your question. What you are mentioning sounds really similar to cutting plane or column generation methods in optimization, so perhaps you want to check those out and see if any active learning approaches have been used. In most cutting plane methods, there is usually an efficient (but ad hoc) way to search for violated constraints, usually found by an optimization subproblem; that could be considered similar to active learning but I'm not sure how a canonical active learning approach would look different.