  Due to the expanding scope of machine learning (ML) to the fields of sensor
networking, cooperative robotics and many other multi-agent systems,
distributed deployment of inference algorithms has received a lot of attention.
These algorithms involve collaboratively learning unknown parameters from
dispersed data collected by multiple agents. There are two competing aspects in
such algorithms, namely, intra-agent computation and inter-agent communication.
Traditionally, algorithms are designed to perform both synchronously. However,
certain circumstances need frugal use of communication channels as they are
either unreliable, time-consuming, or resource-expensive. In this paper, we
propose gossip-based asynchronous communication to leverage fast computations
and reduce communication overhead simultaneously. We analyze the effects of
multiple (local) intra-agent computations by the active agents between
successive inter-agent communications. For local computations, Bayesian
sampling via unadjusted Langevin algorithm (ULA) MCMC is utilized. The
communication is assumed to be over a connected graph (e.g., as in
decentralized learning), however, the results can be extended to coordinated
communication where there is a central server (e.g., federated learning). We
theoretically quantify the convergence rates in the process. To demonstrate the
efficacy of the proposed algorithm, we present simulations on a toy problem as
well as on real world data sets to train ML models to perform classification
tasks. We observe faster initial convergence and improved performance accuracy,
especially in the low data range. We achieve on average 78% and over 90%
classification accuracy respectively on the Gamma Telescope and mHealth data
sets from the UCI ML repository.
