# Deep Learning with Differential Privacy

https://arxiv.org/pdf/1607.00133.pdf

This paper proposes a new algorithm which allows us to train a deep neural network under a modest privacy budget. It offers protection against a strong adversary with full knowledge of the training mechanism and access to the model's parameters.

https://arxiv.org/pdf/1607.00133.pdf

Note that:

- We say that two of sets are adjacent if they differ in a single entry, that is, if one image-label pair is present in one set and absent in the other.
- $e^\epsilon$is the exponential function applied to the parameter$\epsilon > 0$. If$\epsilon$is very close to 0, then$e^\epsilon$is very close to 1, so the probabilities are very similar. The bigger$\epsilon$is, the more the probabilities can differ.
- This paper uses the variant, which allows for the possibility that plain$\epsilon$-differential privacy is broken with probability$\delta$.

https://arxiv.org/pdf/1607.00133.pdf

The algorithm is very similar to the traditional SGD algorithm with few exceptions:

- 1.To guarantee our model is differentially private, we need to bound the influence of each individual example on our model. Thus, , we clip each gradient in l2 norm.
- 2.The algorithm adds noise at lot-level. Lots are similar to a batches, but, to limit the memory consumption, we may set the batch size much smaller than the lot size. We perform the computation in batches, then group several batches into a lot for adding noise.
- 3.The algorithm computes the overall privacy cost of the train.