Parallelisability of Particle-MALA

Determine whether the Particle-MALA algorithm introduced for Feynman–Kac models can be parallelised within the divide-and-conquer sequential Monte Carlo framework of Corenflos et al. (2022), despite the need to marginalise across two time steps rather than one.

Background

The paper proposes Particle-aMALA and shows it can be incorporated into the divide-and-conquer sequentialised methodology of Corenflos et al. (2022) to reduce per-update cost on parallel architectures. The smoothing-gradient variant (Particle-aMALA+) is also argued to likely permit such parallelisation.

However, Particle-MALA differs because its construction marginalises auxiliary variables across two consecutive time steps, which may break the locality required by the parallel divide-and-conquer scheme. The authors explicitly note uncertainty about whether Particle-MALA can be parallelised for this reason, leaving the question unresolved.

References

It is however less clear that Particle-MALA is parallelisable, as the marginalisation has to be done across two time steps rather than one as presented in Section~\ref{subsec:particlemala}.

— Particle-MALA and Particle-mGRAD: Gradient-based MCMC methods for high-dimensional state-space models  (2401.14868 - Corenflos et al., 2024) in Section 6, Extensions (Conclusion)