Summary of issue:
Given a model trained on some input and output data, I'd like to be able to then query the model with a subset of input data, and return a set of missing inputs that would give an optimal output (based on the cost function the model was trained on).
We have a series of stores in different locations. The profit of each is affected by the same set of factors (price of beans, utility bills, staffing, etc).
A model is trained on all the data, with location being one of the input parameters. After training, the model would then be queried by supplying the location (definitely) and optionally some set of the remaining inputs.
The output would be the remaining (missing) inputs that would represent the optimal combination, based on the cost function used in training (profit).
E.g. Inputs are that the store is in Kansas and we pay our staff $100/hour. Output is the optimal wage to offer staff.
What would be some good candidate approaches for this kind of problem?
From what I've researched so far, it seems like recommender systems could be appropriate: (collaborative filtering or restricted Boltzman machine). But are there any "de-facto" solutions for this kind of problem? Any suggestions of what might be promising?