TensorFlow RandomForest vs Deep learning
A useful rule for beginning training models, is not to begin with the more complex methods, for example, a Linear model, which you will be able to understand and debug more easily.
In case you continue with the current methods, some ideas:

Check the initial weight values (init them with a normal distribution)
As a previous poster said, diminish the learning rate
Do some additional checking on the data, check for NAN and outliers, the current models could be more sensitive to noise. Remember, garbage in, garbage out.
I am using TensorFlow for training model which has 1 output for the 4 inputs. The problem is of regression.
I found that when I use RandomForest to train the model, it quickly converges and also runs well on the test data. But when I use a simple Neural network for the same problem, the loss(Random square error) does not converge. It gets stuck on a particular value. 
I tried increasing/decreasing number of hidden layers, increasing/decreasing learning rate. I also tried multiple optimizers and tried to train the model on both normalized and non-normalized data. 
I am new to this field but the literature that I have read so far vehemently asserts that the neural network should marginally and categorically work better than the random forest.
What could be the reason behind non-convergence of the model in this case?