Decentralized Optimization Resilient Against Local Data Poisoning Attacks

In this article, we study the problem of decentralized optimization in the presence of adversarial attacks. In this problem, we consider a collection of nodes connected through a network, each equipped with a local function. These nodes are asked to collaboratively compute the global optimizer, i.e., the point that minimizes the aggregated local functions, using their local information and messages exchanged with their neighbors. Moreover, each node should agree on the said minimizer despite an adversary that can arbitrarily change the local functions of a fraction of the nodes. We present, the resilient averaging gradient descent (RAGD) algorithm, a decentralized, consensus+outlier filtering algorithm that is resilient to such attacks on local functions. We demonstrate that, as long as the portion of attacked nodes does not exceed a given threshold, RAGD guarantees that all nodes will be able to have a good estimate of the said minimizer. We verify the performance of the RAGD algorithm via numerical examples.