DIFF2: Differential Private Optimization via Gradient Differences for Nonconvex Distributed Learning

• URL: http://arxiv.org/abs/2302.03884v2
• Date: Sat, 3 Jun 2023 12:39:11 GMT
• Title: DIFF2: Differential Private Optimization via Gradient Differences for Nonconvex Distributed Learning
• Authors: Tomoya Murata and Taiji Suzuki
• Abstract summary: In the previous work, the best known utility bound is $widetilde O(d2/3/(nvarepsilon_mathrmDP)4/3)$. We propose a new differential private framework called mphDIFF2 (DIFFerential private via DIFFs) that constructs a differential private framework. $mphDIFF2 with a global descent achieves the utility of $widetilde O(d2/3/(nvarepsilon_mathrmDP)4/3
• Score: 58.79085525115987
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Differential private optimization for nonconvex smooth objective is considered. In the previous work, the best known utility bound is $\widetilde O(\sqrt{d}/(n\varepsilon_\mathrm{DP}))$ in terms of the squared full gradient norm, which is achieved by Differential Private Gradient Descent (DP-GD) as an instance, where $n$ is the sample size, $d$ is the problem dimensionality and $\varepsilon_\mathrm{DP}$ is the differential privacy parameter. To improve the best known utility bound, we propose a new differential private optimization framework called \emph{DIFF2 (DIFFerential private optimization via gradient DIFFerences)} that constructs a differential private global gradient estimator with possibly quite small variance based on communicated \emph{gradient differences} rather than gradients themselves. It is shown that DIFF2 with a gradient descent subroutine achieves the utility of $\widetilde O(d^{2/3}/(n\varepsilon_\mathrm{DP})^{4/3})$, which can be significantly better than the previous one in terms of the dependence on the sample size $n$. To the best of our knowledge, this is the first fundamental result to improve the standard utility $\widetilde O(\sqrt{d}/(n\varepsilon_\mathrm{DP}))$ for nonconvex objectives. Additionally, a more computational and communication efficient subroutine is combined with DIFF2 and its theoretical analysis is also given. Numerical experiments are conducted to validate the superiority of DIFF2 framework.

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