loss bounded below when using MSE regardless of the model I choose, is this normal? I've been experimenting with regression models and when checking the loss of some models (MLP, RNN, CNN) I constructed using MSE, the evaluation loss is bounded below by 1.1331, and the training loss is bounded below by 1.1101 (except for the MLP model which has higher bounds)

All 3 models are using the same test/ train data. Is this to be expected? I feel that the models reach the bound very quickly and there must be something going wrong.

Yes, that is completely normal. Any data generating process with noise will have a limit to predictability. If you predict a series of equally probable $0$s and $1$s (a fair coin), you can't do better than always predicting $0.5$, for a best possible MSE of $0.25$. There are very few situations where you can predict perfectly.
