Summary of Differential Private Stochastic Optimization with Heavy-tailed Data: Towards Optimal Rates, by Puning Zhao et al.
Differential Private Stochastic Optimization with Heavy-tailed Data: Towards Optimal Rates
by Puning Zhao, Jiafei Wu, Zhe Liu, Chong Wang, Rongfei Fan, Qingming Li
First submitted to arxiv on: 19 Aug 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Cryptography and Security (cs.CR); Data Structures and Algorithms (cs.DS)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary A machine learning educator writing for a technical audience can generate a medium-difficulty summary as follows: This paper explores convex optimization problems under differential privacy (DP) with heavy-tailed gradients, addressing the existing works’ suboptimal rates. The main obstacle is that existing gradient estimators have suboptimal tail properties, resulting in a superfluous factor of d in the union bound. To achieve optimal rates of DP optimization with heavy-tailed gradients, this paper proposes two algorithms: a simple clipping approach and an iterative updating method. The clipping approach achieves a population risk of (+(/n)^{1-1/p}) under bounded p-th order moments of gradients, while the iterative updating method achieves this rate for all ε ≤ 1. The results significantly improve over existing methods and match the minimax lower bound in [Kamath et al., 2022], indicating that the theoretical limit of stochastic convex optimization under DP is achievable. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper studies how to solve a type of math problem (convex optimization) while keeping the solution private. The big challenge is that when the math problems have “heavy-tailed” gradients, previous methods don’t work well. To fix this, the authors propose two new ways to solve these problems: one simple and one more complex. These new methods are better than what came before and even match a theoretical limit for solving these kinds of problems. |
Keywords
» Artificial intelligence » Machine learning » Optimization
