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Privacy-Preserving Distributed Optimization and Learning

Ziqin Chen, Yongqiang Wang

TL;DR

The paper addresses privacy concerns in distributed optimization and learning where messages reveal private data. It surveys cryptographic approaches (e.g., homomorphic encryption, secure MPC) and differential privacy frameworks, arguing that differential privacy offers practical scalability in high-dimensional problems. It presents DP algorithms for offline optimization, noncooperative NE seeking, and online learning, including $\\epsilon$-DP and local $\\epsilon_i$-DP with finite budgets, and demonstrates convergence results such as $x^*$-convergence under DP. It also provides real-world applications on logistic regression and CNN training and discusses open challenges and directions for achieving stronger privacy without sacrificing convergence speed.

Abstract

Distributed optimization and learning has recently garnered great attention due to its wide applications in sensor networks, smart grids, machine learning, and so forth. Despite rapid development, existing distributed optimization and learning algorithms require each agent to exchange messages with its neighbors, which may expose sensitive information and raise significant privacy concerns. In this survey paper, we overview privacy-preserving distributed optimization and learning methods. We first discuss cryptography, differential privacy, and other techniques that can be used for privacy preservation and indicate their pros and cons for privacy protection in distributed optimization and learning. We believe that among these approaches, differential privacy is most promising due to its low computational and communication complexities, which are extremely appealing for modern learning based applications with high dimensions of optimization variables. We then introduce several differential-privacy algorithms that can simultaneously ensure privacy and optimization accuracy. Moreover, we provide example applications in several machine learning problems to confirm the real-world effectiveness of these algorithms. Finally, we highlight some challenges in this research domain and discuss future directions.

Privacy-Preserving Distributed Optimization and Learning

TL;DR

The paper addresses privacy concerns in distributed optimization and learning where messages reveal private data. It surveys cryptographic approaches (e.g., homomorphic encryption, secure MPC) and differential privacy frameworks, arguing that differential privacy offers practical scalability in high-dimensional problems. It presents DP algorithms for offline optimization, noncooperative NE seeking, and online learning, including -DP and local -DP with finite budgets, and demonstrates convergence results such as -convergence under DP. It also provides real-world applications on logistic regression and CNN training and discusses open challenges and directions for achieving stronger privacy without sacrificing convergence speed.

Abstract

Distributed optimization and learning has recently garnered great attention due to its wide applications in sensor networks, smart grids, machine learning, and so forth. Despite rapid development, existing distributed optimization and learning algorithms require each agent to exchange messages with its neighbors, which may expose sensitive information and raise significant privacy concerns. In this survey paper, we overview privacy-preserving distributed optimization and learning methods. We first discuss cryptography, differential privacy, and other techniques that can be used for privacy preservation and indicate their pros and cons for privacy protection in distributed optimization and learning. We believe that among these approaches, differential privacy is most promising due to its low computational and communication complexities, which are extremely appealing for modern learning based applications with high dimensions of optimization variables. We then introduce several differential-privacy algorithms that can simultaneously ensure privacy and optimization accuracy. Moreover, we provide example applications in several machine learning problems to confirm the real-world effectiveness of these algorithms. Finally, we highlight some challenges in this research domain and discuss future directions.
Paper Structure (31 sections, 1 theorem, 10 equations, 1 figure, 5 tables, 6 algorithms)

This paper contains 31 sections, 1 theorem, 10 equations, 1 figure, 5 tables, 6 algorithms.

Table of Contents

  1. Privacy-Preserving Distributed Optimization and Learning
  2. Introduction
  3. Literature Review
  4. Homomorphic encryption
  5. Secure multi-party computation
  6. Differential privacy
  7. Other privacy-preserving approaches
  8. Background
  9. Distributed optimization and learning
  10. Distributed offline optimization
  11. Noncooperative game.
  12. Aggregative games
  13. Distributed online learning and optimization
  14. Differential privacy
  15. DP in distributed offline optimization
  16. ...and 16 more sections

Key Result

Lemma 1

huang2015 At each iteration $t$, if each agent adds a noise vector $\chi_{t}\in \mathbb{R}^{n}$ consisting of $n$ independent Laplace noises with parameter $\nu_{t}$ such that $\sum_{t=1}^{T}\frac{\delta_{t}}{\nu_{t}}\leq \epsilon$, then the randomized iterative algorithm $\mathcal{A}(\cdot)$ is $\e

Figures (1)

  • Figure 1: Comparison of Algorithm \ref{['ogradienttracking']} with existing DP solutions for distributed learning and optimization, including the DiaDSP algorithm in ding2021, the Algorithm \ref{['tailoring2']} from Wangtailoring2023, the DP distributed optimization algorithm in huang2015, the distributed online optimization algorithm in xiong2020, and Algorithm \ref{['onlinegradient']} from Chengradient2023. To ensure a fair comparison, the privacy budget for these algorithms is set as the maximum $\epsilon_{i}$ across all agents used in Algorithm \ref{['ogradienttracking']}, which corresponds to the weakest level of privacy protection among all agents. Moreover, the conventional Push-Pull gradient-tracking algorithm in pushpull was also evaluated under the same DP noises as those used in Algorithm \ref{['ogradienttracking']}.

Theorems & Definitions (11)

  • Definition 1: Nash equilibrium
  • Definition 2: Adjacency
  • Definition 3: $\epsilon$-Differential Privacy
  • Definition 4: $(\epsilon,\delta)$-differential privacy
  • Definition 5
  • Lemma 1
  • Definition 6: Adjacency in distributed offline optimization
  • Remark 1
  • Definition 7: Adjacency in noncooperative game
  • Definition 8: Adjacency in LDP-distributed online learning
  • ...and 1 more