I was reading about the minimum squared error(MSE) in the TensorwFlow (tf) user document.

You can use MSE when doing regression, believing that your target, conditioned on the input, is normally distributed, and want large errors to be significantly (quadratically) more penalized than small ones.

According to your example , and as mentioned in the image above :

y_true is y and y~i is equals to y_pred , so it will calculate the loss every epoch in order to get the minimum value that means , y_true will be somehow closer to y_pred