Loss function when the output is a single probability
At first I was going to say:


  It doesn't make sense to use use cross entropy loss in a regression
  problem!
  
  See explanation here.


But then I realised that if you are really trying to do regression on probabilities it could have some sense. 

But still, why would you use it instead of L1, L2? So maybe try it and let me know if it works better!