The RAM utilization is expected to increase significantly.
This is because there are multiple number of complex mathematical calculation (e.g. matrix multiplications, matrix inverses, activation function calculation, calculation of gradients) needed to train/test any deep neural network.
Having said that, you can run the trainings on a GPU, which would not only not use RAM, but also increase the speed of training (since, GPUs are best fit for such jobs). You can look at an example on how to train RL netowrks on GPU here.