Q:

Deep Learning: Use L2 and Dropout Regularization Simultaneously?

Is there a theoretical basis against using both L2 and Dropout regularization simultaneously for training a deep neural network?  They are both related but could they be complementary if used together?

A:

The paper {1} that introduced dropout combined dropout with L2:

We found that dropout combined with max-norm regularization gives the
  lowest generalization error.

{1} Srivastava, Nitish, Geoffrey E. Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. "Dropout: a simple way to prevent neural networks from overfitting." Journal of Machine Learning Research 15, no. 1 (2014): 1929-1958. http://jmlr.org/papers/volume15/srivastava14a.old/srivastava14a.pdf

