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Confusing equation in ch6 #53

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WCY-dt opened this issue Oct 29, 2024 · 0 comments · May be fixed by #54
Open

Confusing equation in ch6 #53

WCY-dt opened this issue Oct 29, 2024 · 0 comments · May be fixed by #54

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@WCY-dt
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WCY-dt commented Oct 29, 2024

In Theorem 5 (Advanced Composition) and Theorem 6 (Approximate Advanced Composition), according to Theorem 3.20 in 1 or p121 in 2, I think $\epsilon^\prime$ should be

$$ \epsilon^\prime = \sqrt{2k\ln\left(\frac{1}{\delta^\prime}\right)}\cdot\epsilon + k\epsilon\left(\text{e}^\epsilon - 1\right) $$

Reference 1 gives proof of this.

Footnotes

  1. Dwork, Cynthia, 和Aaron Roth. The Algorithmic Foundations of Differential Privacy. Vol 9, 2013. http://www.nowpublishers.com/articles/foundations-and-trends-in-theoretical-computer-science/TCS-042. ↩ ↩2

  2. Cowan, Ethan, Michael Shoemate和Mayana Pereira. Hands-On Differential Privacy. ↩
@WCY-dt WCY-dt linked a pull request Oct 29, 2024 that will close this issue
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Update theorem 5 & 6 in ch6 WCY-dt/programming-dp
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