I am working with a dataset where I want to minimize levels of a variable, which we can call V1. I have other variables in this dataset, which we can call V2-V10. Variables V2-V5 have been determined to be controllable, meaning that we can manually change levels of these variables. Each variable is continuous (float).
My goal is to tweak levels of V2-V5, such that I minimize the levels of V1.
My thought process is to construct a model that treats V1 as the response, and V2-V10 as explanatories. I've fit an XGBRegressor() model.
From there, I am thinking to introduce some kind of optimization algorithm that tweaks levels of the controllable variables (V2-V5) such that we are minimizing levels of the response (V1).
Assuming that the model has been fit, what methods or algorithms exist for solving this further? Is this thought process correct, or is there a better way to solve? Python methods are preferred.