what is the optimal RDP order?

[carlodavid012]

when i use compute_dp_sgd_privacy, it shows this result. I know the epsilon is the strength of the privacy guarantee, but what does optimal RDP order means?

compute_dp_sgd_privacy.compute_dp_sgd_privacy(n=len(training_sequences), batch_size=250, noise_multiplier=1.3, epochs=15, delta=1e-5)

Output:

DP-SGD with sampling rate = 1.67% and noise_multiplier = 1.3 iterated over 900 steps satisfies differential privacy with eps = 2.46 and delta = 1e-05.
The optimal RDP order is 10.0.
(2.4614490035755816, 10.0)

[jmg-74]

Hi @carlodavid012.
"Classical" (epsilon, delta)-DP is our purpose here, but (alpha, epsilon)-Rényi DP has to be used to compute a tighter bound than the one get by classical DP composition.
Be aware that epsilon values are not the same in both approaches. The former is the 2.46 answer, the latter (the "RDP epsilon") is just used for calculation but not so easy to interpret. That's certainly why it is hidden here. There is an infinity of (alpha, RDP-epsilon) tuples from each one a "classical" epsilon can be deduced. The alpha value which one obtain the optimal "classical" epsilon value is indicated in the answer, this is 10.0 in your example.
I wrote a Jupyter notebook about those computations. You can find it here but it is still a draft and there's no guarantee it will remain available, so download it if necessary. There is also a html version if you don't have a Jupyter server.
I hope it helps you. But I'm just a student, so take care with info in notebook and those given here.

[jmg-74]

In addition, there is a greate explanation here:
https://github.com/tensorflow/privacy/tree/master/tutorials/walkthrough
Regards.

[carlodavid012]

thanks for the answer 👍 @jmg-74

[xuatpham]

Thank you @jmg-74