Lower loss always better for Probabilistic loss functions?
Consider loss to be something akin to implied variability of your model. When loss is extremely high, your model's output could be just about anything. As the loss lowers, your model is becoming more confident in its output and will be able to give similar output classification/regressions even if the initial weights or input data is slightly different. Lower loss in the training set is always a good thing so long as you are seeing a subsequent decrease in the loss of the validation set. As soon as that validation loss starts to stagnate though, I like to save the model and quit. Usually at this point you could get a little better loss, but it tends to just be overfitting and doesn't help any on the test set.