I found people used deep neural network to get optimal policy by solving a nonconvex optimization problem. Moreover, they didn't use any set of training data and claimed that it's the difference between their approach and the supervised learning. I wonder can people set loss function of neural network by themselves instead of choosing cross entropy or mean square error?
My experience in machine learning is very limited. I audited two machine learning courses offered by applied math department in my school. I read twenty or more papers on the application of machine learning. I began to use Keras very recently.