Generalizing Parallel Replica Dynamics: Trajectory Fragments, Asynchronous Computing, and PDMPs

TL;DR

This paper generalizes Parallel Replica Dynamics by introducing a trajectory fragment framework and new algorithms for Markov processes, ensuring consistency in both synchronous and asynchronous settings.

Contribution

It presents a novel trajectory fragment framework and a consistency condition, enabling the design of new parallel algorithms for Markov processes.

Findings

Framework guarantees consistency of algorithms

New algorithms for piecewise deterministic Markov processes

Applicable to both synchronous and asynchronous computing

Abstract

We study the Parallel Replica Dynamics in a general setting. We introduce a trajectory fragment framework that can be used to design and prove consistency of Parallel Replica algorithms for generic Markov processes. We use our framework to formulate a novel condition that guarantees an asynchronous algorithm is consistent. Exploiting this condition and our trajectory fragment framework, we present new synchronous and asynchronous Parallel Replica algorithms for piecewise deterministic Markov processes.