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Deep Learning with Differential Privacy

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

Summary

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.

Differential Privacy

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.
  • eϵe^\epsilon
    is the exponential function applied to the parameter
    ϵ>0\epsilon > 0
    . If
    ϵ\epsilon
    is very close to 0, then
    eϵe^\epsilon
    is very close to 1, so the probabilities are very similar. The bigger
    ϵ\epsilon
    is, the more the probabilities can differ.
  • This paper uses the variant, which allows for the possibility that plain
    ϵ\epsilon
    -differential privacy is broken with probability
    δ\delta
    .

The Algorithm

https://arxiv.org/pdf/1607.00133.pdf
The algorithm is very similar to the traditional SGD algorithm with few exceptions:
  1. 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. 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. 3.
    The algorithm computes the overall privacy cost of the train.