Resilient Distributed Diffusion in Networks With Adversaries

Abstract

In this paper, we study resilient distributed diffusion for multi-task estimation in the presence of adversaries where networked agents must estimate distinct but correlated states of interest by processing streaming data. We show that in general diffusion strategies are not resilient to malicious agents that do not adhere to the diffusion-based information processing rules. In particular, by exploiting the adaptive weights used for diffusing information, we develop time-dependent attack models that drive normal agents to converge to states selected by the attacker. We show that an attacker that has complete knowledge of the system can always drive its targeted agents to its desired estimates. Moreover, an attacker that does not have complete knowledge of the system including streaming data of targeted agents or the parameters they use in diffusion algorithms, can still be successful in deploying an attack by approximating the needed information. The attack models can be used for both stationary and non-stationary state estimation. In addition, we present and analyze a resilient distributed diffusion algorithm that is resilient to any data falsification attack in which the number of compromised agents in the local neighborhood of a normal agent is bounded. The proposed algorithm guarantees that all normal agents converge to their true target states if appropriate parameters are selected. We also analyze trade-off between the resilience of distributed diffusion and its performance in terms of steady-state mean-square-deviation (MSD) from the correct estimates. Finally, we evaluate the proposed attack models and resilient distributed diffusion algorithm using stationary and nonstationary multi-target localization.

Resilient Distributed Diffusion for Multi-Robot Systems Using Centerpoint

“…To achieve resilient optimization, one approach is to discard cooperation with possible Byzantine neighbors. In [7], a resilient diffusion algorithm has been proposed in which normal agents discard information from a certain number of neighbors, which might include Byzantine agents, in the aggregation step. However, the performance of the algorithm depends highly on the accurate estimation of the number of adversarial agents, which is usually unknown.…”

“…However, a single Byzantine agent can drive the output of the weighted average-based aggregation to an arbitrary value as shown in [6, Lemma 1], and hence, prevent the normal agent from converging to the target state. Moreover, in case of adaptive weights, time-dependent Byzantine attack proposed in [7] can disrupt the convergence of normal nodes.…”

“…Although the cooperation among agents helps improve the overall learning performance, the aggregation step in distributed diffusion is susceptible to attacks where non-cooperative or adversarial neighbors sharing wrong information can disrupt the convergence of the algorithm. It has been shown (for both fixed and adaptive weights) that a single misbehaving agent can adversely impact the convergence of remaining agents to the desired target state [6], [7]. Therefore, it is crucial to design a resilient aggregation rule for distributed diffusion.…”

Byzantine Resilient Distributed Multi-Task Learning

“…Fault-tolerance for MTL is discussed in [5], focusing on dropped nodes that occasionally stop sending information to their neighbors. In [16], the relationship promoted by measuring the quadratic distance between two model parameters for distributed MTL is shown to be vulnerable to gradient-based attacks, and a Byzantine resilient distributed MTL algorithm is proposed for regression problems to cope with such attacks. The proposed algorithm relies on a user-defined parameter F to filter out information from F neighbors in the aggregation step and is resilient to F Byzantine neighbors, but requires exponential time with respect to the number of agents.…”

“…In this paper, we propose an online weight adjustment rule for MTL that is guaranteed to achieve resilient distributed MTL for every normal agent using the rule. Compared to [16], the proposed method is suited for both regression and classification problems, is resilient to an arbitrary number of Byzantine agents (without the need to select a pre-defined parameter F bounding the number of Byzantine agents), and has linear time complexity. To the best of our knowledge, this is the first solution that aims to address the Byzantine resilient cooperation in distributed MTL networks via a resilient similarity promoting method.…”