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A survey on secure decentralized optimization and learning

Changxin Liu, Nicola Bastianello, Wei Huo, Yang Shi, Karl H. Johansson

TL;DR

This survey addresses privacy and security in decentralized optimization and learning, detailing how data privacy and model security challenges arise in federated and peer-to-peer setups. It surveys three cryptographic tools—differential privacy, homomorphic encryption, and secret sharing—and explains their integration into privacy-preserving decentralized algorithms across topologies, plus resilient aggregation and consensus methods (e.g., CWMed, Krum, GM, MSR). It analyzes attack models (Byzantine/malicious), resilience metrics (aggregation resilience, graph robustness, cost redundancy), and the implications of data heterogeneity, communication bottlenecks, and resource constraints. The work also outlines future directions, emphasizing simultaneous privacy and resilience, asynchronous operation, attacker detection, side information, blockchain-enabled security, and control applications, to advance practical secure decentralized optimization and learning.

Abstract

Decentralized optimization has become a standard paradigm for solving large-scale decision-making problems and training large machine learning models without centralizing data. However, this paradigm introduces new privacy and security risks, with malicious agents potentially able to infer private data or impair the model accuracy. Over the past decade, significant advancements have been made in developing secure decentralized optimization and learning frameworks and algorithms. This survey provides a comprehensive tutorial on these advancements. We begin with the fundamentals of decentralized optimization and learning, highlighting centralized aggregation and distributed consensus as key modules exposed to security risks in federated and distributed optimization, respectively. Next, we focus on privacy-preserving algorithms, detailing three cryptographic tools and their integration into decentralized optimization and learning systems. Additionally, we examine resilient algorithms, exploring the design and analysis of resilient aggregation and consensus protocols that support these systems. We conclude the survey by discussing current trends and potential future directions.

A survey on secure decentralized optimization and learning

TL;DR

This survey addresses privacy and security in decentralized optimization and learning, detailing how data privacy and model security challenges arise in federated and peer-to-peer setups. It surveys three cryptographic tools—differential privacy, homomorphic encryption, and secret sharing—and explains their integration into privacy-preserving decentralized algorithms across topologies, plus resilient aggregation and consensus methods (e.g., CWMed, Krum, GM, MSR). It analyzes attack models (Byzantine/malicious), resilience metrics (aggregation resilience, graph robustness, cost redundancy), and the implications of data heterogeneity, communication bottlenecks, and resource constraints. The work also outlines future directions, emphasizing simultaneous privacy and resilience, asynchronous operation, attacker detection, side information, blockchain-enabled security, and control applications, to advance practical secure decentralized optimization and learning.

Abstract

Decentralized optimization has become a standard paradigm for solving large-scale decision-making problems and training large machine learning models without centralizing data. However, this paradigm introduces new privacy and security risks, with malicious agents potentially able to infer private data or impair the model accuracy. Over the past decade, significant advancements have been made in developing secure decentralized optimization and learning frameworks and algorithms. This survey provides a comprehensive tutorial on these advancements. We begin with the fundamentals of decentralized optimization and learning, highlighting centralized aggregation and distributed consensus as key modules exposed to security risks in federated and distributed optimization, respectively. Next, we focus on privacy-preserving algorithms, detailing three cryptographic tools and their integration into decentralized optimization and learning systems. Additionally, we examine resilient algorithms, exploring the design and analysis of resilient aggregation and consensus protocols that support these systems. We conclude the survey by discussing current trends and potential future directions.
Paper Structure (87 sections, 2 theorems, 51 equations, 7 figures, 9 tables, 3 algorithms)

This paper contains 87 sections, 2 theorems, 51 equations, 7 figures, 9 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Organization of the paper
  3. Related survey papers
  4. Notation
  5. Decentralized optimization and learning
  6. Optimization problem and system architectures
  7. Federated optimization
  8. Communications bottleneck
  9. Resources heterogeneity
  10. One last challenge: statistical heterogeneity
  11. Distributed optimization
  12. Distributed gradient descent
  13. Gradient tracking
  14. Distributed dual averaging
  15. Alternating direction method of multipliers
  16. ...and 72 more sections

Key Result

Lemma 1

Consider the Laplace mechanism for answering the query $r:\mathcal{D}\rightarrow \mathbb{R}^d$: where $\nu_i, \forall i$ are independent and have the following probability density function $e^{-\frac{{x}}{\lambda}}/(2\lambda)$ where $\lambda>0$ is a scale parameter. The mechanism $\mathcal{M}_L$ is ($\Delta_1/\lambda,0$)-DP where $\Delta_1$ denotes the $\ell_1$-sensitivity of $r$, i.e., $\Delt

Figures (7)

  • Figure 1: The intersection of machine learning, decentralized optimization, and CPS security.
  • Figure 2: Organization of the paper.
  • Figure 3: Depictions of the three main architectures for optimization and learning.
  • Figure 4: An illustration of client drift.
  • Figure 5: An illustration of the privacy-accuracy-efficiency trade-off.
  • ...and 2 more figures

Theorems & Definitions (13)

  • Example 1: Empirical risk minimization
  • Definition 1: Differential privacy
  • Lemma 1: Laplace mechanism
  • Lemma 2: Gaussian mechanism
  • Example 2: Differentially private gradient descent
  • Example 3: Paillier cryptosystem and its application in privacy-preserving optimization
  • Example 4: Privacy-preserving aggregation based on secret sharing emekcci2007privacy
  • Example 5: Resilient consensus of probability vectors vaidya2013byzantine
  • Definition 2: $n_f$-safe point
  • Definition 3: Concentration
  • ...and 3 more