Decentralized Langevin Dynamics over a Directed Graph

The prevalence of technologies in the space of the Internet of Things and use of multi-processing computing platforms to aid in the computation required to perform learning and inference from large volumes of data has necessitated the extensive study of algorithms on decentralized platforms. In these settings, computing nodes send and receive data across graph-structured communication links, and using a combination of local computation and consensus-seeking communication, cooperately solve a problem of interest. Recently, Langevin dynamics as a tool for high dimensional sampling and posterior Bayesian inference has been studied in the context of a decentralized operation. However, this work has been limited to undirected graphs, wherein all communication is two-sided, i.e., if node A can send data to node B, then node B can also send data to node A. We extend the state of the art in considering Langevin dynamics on directed graphs.