On parallel implementation of Sequential Monte Carlo methods: the island particle model

TL;DR

This paper explores the parallelization of Sequential Monte Carlo methods by dividing the particle population into islands, analyzing their dynamics, interactions, and efficiency improvements through theoretical and experimental results.

Contribution

It introduces a framework for parallelizing Feynman-Kac particle approximations using island models, with explicit relations and conditions for effective interactions.

Findings

Island-based parallelization can improve computational efficiency.

Interactions between islands can be beneficial under certain conditions.

Theoretical results are validated through Monte Carlo experiments.

Abstract

The approximation of the Feynman-Kac semigroups by systems of interacting particles is a very active research field, with applications in many different areas. In this paper, we study the parallelization of such approximations. The total population of particles is divided into sub-populations, referred to as \emph{islands}. The particles within each island follow the usual selection / mutation dynamics. We show that the evolution of each island is also driven by a Feynman-Kac semigroup, whose transition and potential can be explicitly related to ones of the original problem. Therefore, the same genetic type approximation of the Feynman-Kac semi-group may be used at the island level; each island might undergo selection / mutation algorithm. We investigate the impact of the population size within each island and the number of islands, and study different type of interactions. We find conditions under which introducing interactions between islands is beneficial. The theoretical results are supported by some Monte Carlo experiments.