The Power of an Adversary in Glauber Dynamics

TL;DR

This paper investigates how adversarial control of nodes in Glauber dynamics affects the system's global properties, revealing the robustness limits of these dynamics against corruption.

Contribution

It introduces a model of corrupted Glauber dynamics with adversarial control and analyzes its impact on system convergence and statistics.

Findings

Controlling a small fraction of nodes can significantly alter system statistics.

A certain number of controlled nodes can prevent approximate convergence.

Results relate to robustness of sampling methods and robust inference.

Abstract

Glauber dynamics are a natural model of dynamics of dependent systems. While originally introduced in statistical physics, they have found important applications in the study of social networks, computer vision and other domains. In this work, we introduce a model of corrupted Glauber dynamics whereby instead of updating according to the prescribed conditional probabilities, some of the vertices and their updates are controlled by an adversary. We study the effect of such corruptions on global features of the system. Among the questions we study are: How many nodes need to be controlled in order to change the average statistics of the system in polynomial time? And how many nodes are needed to obstruct approximate convergence of the dynamics? Our results can be viewed as studying the robustness of classical sampling methods and are thus related to robust inference. The proofs connect to classical theory of Glauber dynamics from statistical physics.