Our team developed a granular individual customer level ML model which can predict the revenue generated (dependent variable) for given amount of promotions (Calls, emails, meetings, impressions etc.) and few categorical details of customers (address, designation, segment etc.).
Once the model is in place, we were supposed to give the "optimal" promotions at which the revenue is maximized at individual level with certain constraints (like overall promotions spend under certain amount etc. we have costs for each promotions so essentially the constraints are like bounds on the independent feature values).
At present we simulate all possible promotional values for call, emails, meetings, impressions etc. (categorical variables do not change for individual customers) and get the best possible revenue case for each individual by model prediction.
The problem with this present approach is it is a brute force method. We have ~1 million customers and simulating for various quantities of promotional entries (lots of combinations) will end up with huge data and the prediction itself is taking significant time.
Given this is a simple maximization problem but one which have ML model prediction output (neural network in our case) as the function for given input features, We are looking for any optimizers that can solve this without need of a data simulation. It is like a solver function in excel where objective function is a ML model prediction.
A simple analogy - California Housing Prices is a well known ML regression problem. Assuming we have a well developed model (non-parametric model say a neural network), how can we estimate the best feature values (with some constraints) at which the house price is maximum for each county (imagine the data to have county information as well) without explicitly simulating the data.