What solution to apply for finding the optimal parameters?
It appears that you have a function $f:\mathbb{R}^4 \to \mathbb{R}$ and you want to find $x$ that maximizes $f(x)$, but you cannot compute $f$ directly; you can only obtain a noisy estimate of its value.

Many optimization methods can be adapted to this setting.  A simple thing you could try would be an iterative method like gradient ascent or Newton's method, but with more iterations to account for the noise; the idea is that the noise will average out given enough iterations.

For instance, gradient ascent requires that you be able to compute the gradient $\nabla f (x)$ for any point of your choosing.  In your case, this can be done by estimating

$$\nabla f(x) = ((f(x+e_1)-f(x-e_1))/2, \dots, (f(x+e_4)-f(x-e_4))/2),$$

where $e_1=(1,0,0,0)$, $e_2=(0,1,0,0)$, and so on.  Now given the ability to compute $f$ on a point of your choice, by computing $f$ on 8 inputs, you can estimate $\nabla f(x)$ and then take a single step of gradient ascent; and repeat until convergence.

A more sophisticated approach would be to try using Bayesian optimization, such as Google Vizier.