Vanishing bias of PLA as a standalone projected algorithm

Ascertain whether the Preconditioned Langevin Algorithm, when used as a standalone method with a projection to ensure feasibility on constrained convex domains, has vanishing bias as the step size h → 0 under suitable conditions on the metric M.

Background

The authors note that PLA, as an unadjusted discretization, is likely biased and has not been analyzed in this work as a standalone algorithm with projection. Determining whether the bias vanishes as h → 0 under metric assumptions would clarify its theoretical viability for constrained sampling without a Metropolis correction.

A positive result would suggest a simpler alternative to MAPLA in some settings, while a negative result would delineate the necessity of Metropolis adjustment for accuracy.