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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence / EAAI-20

Differentially Private Empirical Risk Minimization with Smooth Non-Convex Loss Functions: A Non-Stationary View

February 1, 2023

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Authors

Di Wang

State University of New York at Buffalo


Jinhui Xu

State University of New York at Buffalo


DOI:

10.1609/aaai.v33i01.33011182


Abstract:

In this paper, we study the Differentially Private Empirical Risk Minimization (DP-ERM) problem with non-convex loss functions and give several upper bounds for the utility in different settings. We first consider the problem in low-dimensional space. For DP-ERM with non-smooth regularizer, we generalize an existing work by measuring the utility using ℓ2 norm of the projected gradient. Also, we extend the error bound measurement, for the first time, from empirical risk to population risk by using the expected ℓ2 norm of the gradient. We then investigate the problem in high dimensional space, and show that by measuring the utility with Frank-Wolfe gap, it is possible to bound the utility by the Gaussian Width of the constraint set, instead of the dimensionality p of the underlying space. We further demonstrate that the advantages of this result can be achieved by the measure of ℓ2 norm of the projected gradient. A somewhat surprising discovery is that although the two kinds of measurements are quite different, their induced utility upper bounds are asymptotically the same under some assumptions. We also show that the utility of some special non-convex loss functions can be reduced to a level (i.e., depending only on log p) similar to that of convex loss functions. Finally, we test our proposed algorithms on both synthetic and real world datasets and the experimental results confirm our theoretical analysis.

Topics: AAAI

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Di Wang||Jinhui Xu Differentially Private Empirical Risk Minimization with Smooth Non-Convex Loss Functions: A Non-Stationary View Proceedings of the AAAI Conference on Artificial Intelligence (2019) 1182-1189.

Di Wang||Jinhui Xu Differentially Private Empirical Risk Minimization with Smooth Non-Convex Loss Functions: A Non-Stationary View AAAI 2019, 1182-1189.

Di Wang||Jinhui Xu (2019). Differentially Private Empirical Risk Minimization with Smooth Non-Convex Loss Functions: A Non-Stationary View. Proceedings of the AAAI Conference on Artificial Intelligence, 1182-1189.

Di Wang||Jinhui Xu. Differentially Private Empirical Risk Minimization with Smooth Non-Convex Loss Functions: A Non-Stationary View. Proceedings of the AAAI Conference on Artificial Intelligence 2019 p.1182-1189.

Di Wang||Jinhui Xu. 2019. Differentially Private Empirical Risk Minimization with Smooth Non-Convex Loss Functions: A Non-Stationary View. "Proceedings of the AAAI Conference on Artificial Intelligence". 1182-1189.

Di Wang||Jinhui Xu. (2019) "Differentially Private Empirical Risk Minimization with Smooth Non-Convex Loss Functions: A Non-Stationary View", Proceedings of the AAAI Conference on Artificial Intelligence, p.1182-1189

Di Wang||Jinhui Xu, "Differentially Private Empirical Risk Minimization with Smooth Non-Convex Loss Functions: A Non-Stationary View", AAAI, p.1182-1189, 2019.

Di Wang||Jinhui Xu. "Differentially Private Empirical Risk Minimization with Smooth Non-Convex Loss Functions: A Non-Stationary View". Proceedings of the AAAI Conference on Artificial Intelligence, 2019, p.1182-1189.

Di Wang||Jinhui Xu. "Differentially Private Empirical Risk Minimization with Smooth Non-Convex Loss Functions: A Non-Stationary View". Proceedings of the AAAI Conference on Artificial Intelligence, (2019): 1182-1189.

Di Wang||Jinhui Xu. Differentially Private Empirical Risk Minimization with Smooth Non-Convex Loss Functions: A Non-Stationary View. AAAI[Internet]. 2019[cited 2023]; 1182-1189.


ISSN: 2374-3468


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Copyright 2022, Association for the Advancement of
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101, Palo Alto, California 94303 All Rights Reserved

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