  We investigate the mean star formation rates (SFRs) in the host galaxies of
~3000 optically selected QSOs from the SDSS survey within the Herschel-ATLAS
fields, and a radio-luminous sub-sample, covering the redshift range of z =
0.2-2.5. Using WISE & Herschel photometry (12 - 500{\mu}m) we construct
composite SEDs in bins of redshift and AGN luminosity. We perform SED fitting
to measure the mean infrared luminosity due to star formation, removing the
contamination from AGN emission. We find that the mean SFRs show a weak
positive trend with increasing AGN luminosity. However, we demonstrate that the
observed trend could be due to an increase in black hole (BH) mass (and a
consequent increase of inferred stellar mass) with increasing AGN luminosity.
We compare to a sample of X-ray selected AGN and find that the two populations
have consistent mean SFRs when matched in AGN luminosity and redshift. On the
basis of the available virial BH masses, and the evolving BH mass to stellar
mass relationship, we find that the mean SFRs of our QSO sample are consistent
with those of main sequence star-forming galaxies. Similarly, the
radio-luminous QSOs have mean SFRs that are consistent with both the overall
QSO sample and with star-forming galaxies on the main sequence. In conclusion,
on average QSOs reside on the main sequence of star-forming galaxies, and the
observed positive trend between the mean SFRs and AGN luminosity can be
attributed to BH mass and redshift dependencies.
