Byzantine-Resilient Distributed Hypothesis Testing With Time-Varying Network Topology

Abstract

In this article, we study the problem of distributed hypothesis testing over a network of mobile agents with limited communication and sensing ranges to infer the true hypothesis collaboratively. In particular, we consider a scenario where there is an unknown subset of compromised agents that may deliberately share altered information to undermine the team objective. We propose two distributed algorithms where each agent maintains and updates two sets of beliefs (i.e., probability distributions over the hypotheses), namely <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">local</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">actual</i> beliefs (LB and AB, respectively, for brevity). In both algorithms, at every time step, each agent shares its AB with other agents within its communication range and makes a local observation to update its LB. Then, both algorithms can use the shared information to update ABs under certain conditions. One requires receiving a certain number of shared ABs at <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">each time instant</i> ; the other accumulates shared ABs <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">over time</i> and updates after the number of shared ABs exceeds a prescribed threshold. Otherwise, both algorithms rely on the agent’s current LB and AB to update the new AB. We prove under mild assumptions that the AB for every noncompromised agent converges almost surely to the true hypothesis, without requiring connectivity in the underlying time-varying network topology. Using a simulation of a team of unmanned aerial vehicles aiming to classify adversarial agents among themselves, we illustrate and compare the proposed algorithms. Finally, we show experimentally that the second algorithm consistently outperforms the first algorithm in terms of the speed of convergence.