Regression problem with Deep Learning
The ability of the model to predict negative value for the housing price depends on the data. On the large amount of data, where there are no negative pricing, the model does not predict a negative number. However, in rare case, where the model is not trained well or has not seen such samples, then it is still possible.

The models prediction on the positive value can be still controlled post predictions. Just like using a treshold. y = y if y&gt;0 else 0; Where the housing cost (y) is as it is if it's positive, 0 otherwise.

ReLu function, works in the way you desire. Negative values gets converted to 0 by the activation.


I am not very sure about the Poisson  loss, you may try it.