The next step is to decide how the parameters should be changed such that they minimize the cost function.
The chosen cost function for this problem is
$$ C(\boldsymbol{x}, P) = \frac{1}{N} \sum_i \big(g_t'(x_i, P) - ( -\gamma g_t(x_i, P) \big)^2 $$In order to minimize the cost function, an optimization method must be chosen.
Here, gradient descent with a constant step size has been chosen.