Distributed Bayesian learning via Langevin dynamics

Bayesian learning provides an efficient sampling framework with an in-built uncertainty estimation to perform parameter estimation tasks as a robust alternative to traditional optimization techniques. Langevin dynamics-based Markov Chain Monte Carlo (MCMC) methods have received significant attention to perform such Bayesian sampling. Although the framework itself is highly scalable for large datasets, the computational and time requirements pose a bottleneck when it comes to such datasets. This is primarily due to the gradient computation since Langevin dynamics inherently relies on the gradient information. Furthermore, difficulty arises due to the lack of availability of centralized information at a single server due to physical and privacy constraints. Under such circumstances, often the data is distributed among a network of agents who work in tandem to conclude the best possible common parameters without exchanging the data itself. Here, communication among agents is key, but also poses an additional overhead. Inspired by these non-trivial challenges, we tackle the problem of distributed Bayesian learning among agents with various protocols to reduce the strain of heavy gradient calculation and inter-agent communication while guaranteeing convergence of the estimations in a probabilistic sense. We also establish mathematical guaranties for the rate of convergence of our proposed algorithmic protocols using minimal assumptions on the problem gradient and illustrate our findings with some simple yet conclusive empirical experiments.