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Training Differentially Private Neural Networks with Lottery Tickets

Part of the Lecture Notes in Computer Science book series (LNSC,volume 12973)

Abstract

We propose the differentially private lottery ticket hypothesis (DPLTH). An end-to-end differentially private training paradigm based on the lottery ticket hypothesis, designed specifically to improve the privacy-utility trade-off in differentially private neural networks. DPLTH, using high-quality winners privately selected via our custom score function outperforms current methods by a margin greater than 20%. We further show that DPLTH converges faster, allowing for early stopping with reduced privacy budget consumption and that a single publicly available dataset for ticket generation is enough for enhancing the utility on multiple datasets of varying properties and from varying domains. Our extensive evaluation on six public datasets provides evidence to our claims.

Keywords

  • Differential privacy
  • Lottery ticket hypothesis
  • Differential privacy in neural networks

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Notes

  1. 1.

    Code for DPLTH will be made publicly available at https://github.com/lgondara/DPLTH.

  2. 2.

    As we are only composing two mechanisms, advanced composition is not necessary.

  3. 3.

    https://github.com/google-research/lottery-ticket-hypothesis.

  4. 4.

    https://github.com/tensorflow/privacy.

  5. 5.

    DPLTH consistently selects winning tickets with total parameters \({\le }10\%\) of the full model.

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Acknowledgements

This research is in part supported by a CGS-D award and a discovery grant from Natural Sciences and Engineering Research Council of Canada.

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Correspondence to Lovedeep Gondara .

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Appendix

Appendix

Theorem 1

Phase 2 (Selecting a winning ticket) is (\(\epsilon _1\)) - differentially private.

Proof

We consider the scenario where the EM outputs some element \(r \in \mathcal {R}\) on two neighbouring datasets, \(X,X'\).

$$\begin{aligned} \dfrac{Pr[\mathcal {M}(X,u,\mathcal {R}) = r]}{Pr[\mathcal {M}(X',u,\mathcal {R}) = r]} = \dfrac{\bigg ( \dfrac{\exp (\dfrac{\epsilon _1 u (X,r)}{2 \varDelta u})}{\sum _{r' \in \mathcal {R}} \exp (\dfrac{\epsilon _1 u (X,r')}{2 \varDelta u})} \bigg )}{\bigg ( \dfrac{\exp (\dfrac{\epsilon _1 u (X',r)}{2 \varDelta u})}{\sum _{r' \in \mathcal {R}} \exp (\dfrac{\epsilon _1 u (X',r')}{2 \varDelta u})} \bigg )} \end{aligned}$$
(6)
$$\begin{aligned} = \bigg ( \dfrac{\exp (\dfrac{\epsilon _1 u (X,r)}{2 \varDelta u})}{\exp (\dfrac{\epsilon _1 u (X',r)}{2 \varDelta u})} \bigg ) . \bigg ( \dfrac{\sum _{r' \in \mathcal {R}} \exp (\dfrac{\epsilon _1 u (X,r')}{2 \varDelta u})}{\sum _{r' \in \mathcal {R}} \exp (\dfrac{\epsilon _1 u (X',r')}{2 \varDelta u})} \bigg ) \end{aligned}$$
(7)
$$\begin{aligned} = \exp \bigg ( \dfrac{\epsilon _1 (u(X,r') - u(X',r'))}{2 \varDelta u} \bigg ) . \bigg ( \dfrac{\sum _{r' \in \mathcal {R}} \exp (\dfrac{\epsilon _1 u (X,r')}{2 \varDelta u})}{\sum _{r' \in \mathcal {R}} \exp (\dfrac{\epsilon _1 u (X',r')}{2 \varDelta u})} \bigg ) \end{aligned}$$
(8)
$$\begin{aligned} \le \exp (\dfrac{\epsilon _1}{2}) . \exp (\dfrac{\epsilon _1}{2}) . \bigg ( \dfrac{\sum _{r' \in \mathcal {R}} \exp (\dfrac{\epsilon _1 u (X,r')}{2 \varDelta u})}{\sum _{r' \in \mathcal {R}} \exp (\dfrac{\epsilon _1 u (X',r')}{2 \varDelta u})} \bigg ) \end{aligned}$$
(9)
$$\begin{aligned} \le \exp (\epsilon _1) \end{aligned}$$
(10)

   \(\square \)

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Gondara, L., Carvalho, R.S., Wang, K. (2021). Training Differentially Private Neural Networks with Lottery Tickets. In: Bertino, E., Shulman, H., Waidner, M. (eds) Computer Security – ESORICS 2021. ESORICS 2021. Lecture Notes in Computer Science(), vol 12973. Springer, Cham. https://doi.org/10.1007/978-3-030-88428-4_27

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  • DOI: https://doi.org/10.1007/978-3-030-88428-4_27

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