  We use the approximation-free Bold Diagrammatic Monte Carlo technique to
study the effects of a finite dispersion of the optical phonon mode on the
properties of the Holstein polaron, especially its effective mass. For weak
electron-phonon coupling the effect is very small, but it becomes significant
for moderate and large electron-phonon coupling. The effective mass is found to
increase (decrease) if the phonon dispersion has a negative (positive)
curvature at the centre of the Brillouin zone.
