Active learning for inferring a convex optimization formulation

Question

I was wondering if anybody knows of any relevant references on the general topic of active learning for gradually inferring/updating a convex opt. formulation.

As a specific example, I am thinking of a system where a learner can query an oracle the validity of the current best solution to incrementally learn constraints or coefficients of an LP cost function.

Update

I am interested in problems and methods where we don't have access to the full definition of the problem (e.g. in LP the constraints that define the polytope, or the cost coefficients are unknown). Yet we may be able to iteratively solve the problem by iteratively asking a sequence of questions to an oracle until the last query confirms we have reached an optimal solution (an optimal vertex in LP)

Answer 1

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.