How to optimize input parameters given target and scoring parameters I'm new to machine learning/optimization, so I apologize in advance if this has been answered before. I don't know which search terms to use.

I have a large dataset where I have a number of input parameters $I_1$, ... $I_n$ ($n$ up to 10), a target parameter $T$ and a scoring parameter $S$. There are roughly a million rows of real-life data, where each row has the input parameters, the target parameter and the scoring parameter. The data is operational data from a piece of machinery where $T$ is output power, $S$ is fuel consumption and $I_1$, ... $I_n$ are tuning parameters for the machinery. The relationships of the tuning parameters to $S$ and $T$ are unknown but likely nonlinear. So I basically want to understand how to tune the machinery to produce the desired output power as fuel-efficiently as possible given the parameters I can tune.

What I need is some way of getting to a function where I input $T$ and get out the optimal combination of $I_1$, ... $I_n$ that minimizes $S$ for that value of $T$. I work in Python, and I assume that it's some combination of sklearn and scipy, but I haven't been able to figure out the steps to take for this type of problem. Thanks in advance.
If your data have simple linear relationship (or you can transform it such that this is the case) you can do regression on $T$ and $S$, and after that you should have the linear relationship between input parameters and target parameters. After that you can use scipy minimize or any other library to perform constrained optimization. If I follow from my example my idea would be to perform a predefined trade-off between $T$ and $S$ for example $\max 0.8 T + 0. 2S$. This should be easy to code with scipy.