Disturbance Rejection for Robust Distributed Learning via Time-Vertex Filtering

Distributed learning has attracted considerable interests in literatures because the collaborations of multiple agents would help to solve complicated engineering problems. Robustness issue plays an important role in distributed learning since attacks on agents would strongly affect the convergence performance and even lead the collaboration to an incorrect global solution. In this paper, we consider the attacks as disturbance and propose a joint time-graph filtering to defend against the attacks in distributed learning. The coefficients of joint filtering can be determined based on the coefficients of time-domain and graph-domain filters that are designed separately. If there is no attack in distributed learning, the joint time-graph filtering can also contribute to the convergence performance acceleration. Numerical studies demonstrate that the joint filtering in both time domain and graph domain can defend against attacks with noise and outperforms several existing algorithms.