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Resilient Distributed Optimization for Multi-Agent Cyberphysical Systems

Michal Yemini, Angelia Nedić, Andrea J. Goldsmith, Stephanie Gil

TL;DR

The work tackles resilient distributed optimization in multi-agent cyberphysical systems where some agents behave maliciously. It introduces a trust-informed, adaptive weighting scheme that learns trustworthy neighbors from stochastic inter-agent trust values $\alpha_{ij}(t)$ and filters malicious influence while optimizing the global objective. The authors prove almost-sure and $r$-th mean convergence to the nominal optimum $x_{\mathcal{L}}^{\star}$ and derive finite-time convergence-rate bounds that depend on trust accuracy, topology, and the number of malicious agents, including exponential decay in misclassification probabilities. Numerical experiments in both low- and high-dimensional settings demonstrate recovery of the global optimum even when malicious agents outnumber legitimate ones, underscoring the practical impact of leveraging physical-layer trust information for resilience in distributed optimization.

Abstract

This work focuses on the problem of distributed optimization in multi-agent cyberphysical systems, where a legitimate agent's iterates are influenced both by the values it receives from potentially malicious neighboring agents, and by its own self-serving target function. We develop a new algorithmic and analytical framework to achieve resilience for the class of problems where stochastic values of trust between agents exist and can be exploited. In this case, we show that convergence to the true global optimal point can be recovered, both in mean and almost surely, even in the presence of malicious agents. Furthermore, we provide expected convergence rate guarantees in the form of upper bounds on the expected squared distance to the optimal value. Finally, numerical results are presented that validate our analytical convergence guarantees even when the malicious agents compose the majority of agents in the network and where existing methods fail to converge to the optimal nominal points.

Resilient Distributed Optimization for Multi-Agent Cyberphysical Systems

TL;DR

The work tackles resilient distributed optimization in multi-agent cyberphysical systems where some agents behave maliciously. It introduces a trust-informed, adaptive weighting scheme that learns trustworthy neighbors from stochastic inter-agent trust values and filters malicious influence while optimizing the global objective. The authors prove almost-sure and -th mean convergence to the nominal optimum and derive finite-time convergence-rate bounds that depend on trust accuracy, topology, and the number of malicious agents, including exponential decay in misclassification probabilities. Numerical experiments in both low- and high-dimensional settings demonstrate recovery of the global optimum even when malicious agents outnumber legitimate ones, underscoring the practical impact of leveraging physical-layer trust information for resilience in distributed optimization.

Abstract

This work focuses on the problem of distributed optimization in multi-agent cyberphysical systems, where a legitimate agent's iterates are influenced both by the values it receives from potentially malicious neighboring agents, and by its own self-serving target function. We develop a new algorithmic and analytical framework to achieve resilience for the class of problems where stochastic values of trust between agents exist and can be exploited. In this case, we show that convergence to the true global optimal point can be recovered, both in mean and almost surely, even in the presence of malicious agents. Furthermore, we provide expected convergence rate guarantees in the form of upper bounds on the expected squared distance to the optimal value. Finally, numerical results are presented that validate our analytical convergence guarantees even when the malicious agents compose the majority of agents in the network and where existing methods fail to converge to the optimal nominal points.
Paper Structure (22 sections, 14 theorems, 92 equations, 2 figures, 1 algorithm)

This paper contains 22 sections, 14 theorems, 92 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Paper contribution
  4. Paper organization
  5. Problem Formulation
  6. Trust values
  7. The update rule of agents
  8. The update rule for the legitimate agents
  9. The update rule for the malicious agents
  10. Assumptions on connectivity and objective functions
  11. Research objectives
  12. Algorithm
  13. The weight matrix sequence
  14. Learning the sets of trusted neighbors
  15. Asymptotic Convergence to Optimal Point
  16. ...and 7 more sections

Key Result

Lemma 1

Consider the random variables $\beta_{ij}(t)$ capturing the history of stochastic trust values as defined in eq:betas and let Assumption assumption:trust_observation hold. Then, for every $t\geq 0$ and every $i\in \mathcal{L}$, $j\in\mathcal{N}_i\cap\mathcal{L},$ while for every $t\geq 0$ and every $i\in \mathcal{L},\ j\in \mathcal{N}_i\cap\mathcal{M}$,

Figures (2)

  • Figure 1: Undirected graph $\mathbb{G}$. Two agents are neighbors if they are connected by an edge. Legitimate and malicious agents are depicted by blue and red nodes, respectively. Since every malicious agent is connected to all legitimate agents, all malicious agents are captured by a single node for simplicity of presentation. Edges between legitimate agents are depicted by black solid lines. Edges between legitimate and malicious agents are depicted by red dashed lines.
  • Figure 2: Average $\overline{e}(t)$ as a function of $t$ for $|\mathcal{M}|=15,\:\ell=0.8$.

Theorems & Definitions (27)

  • Definition II.1: $\alpha_{ij}$
  • Lemma 1: Lemma 2 ourTRO
  • Corollary 1
  • proof
  • Lemma 2
  • Corollary 2
  • Lemma 3
  • proof
  • Theorem 1
  • Theorem 2: Convergence a.s. to the optimal point
  • ...and 17 more