  Exploring how radio-emitting active galactic nuclei (AGN) behave and evolve
with time is critical for understanding how AGN feedback impacts galaxy
evolution. In this work, we investigate the relationship between 1.4 GHz radio
continuum AGN luminosity ($L^{\rm AGN}_{\rm 1.4}$), specific black hole
accretion rate (s-BHAR, defined as the accretion luminosity relative to the
galaxy stellar mass) and redshift, for a luminosity-complete sample of
radio-selected AGN in the VLA COSMOS 3 GHz Large Project. The sample was
originally selected from radio-continuum observations at 3 GHz, and includes
about 1800 radio AGN identified via ($>2\sigma$) radio-excess relative to the
infrared-radio correlation of star-forming galaxies. We further select a
subsample of over 1200 radio AGN that is complete in $L^{\rm AGN}_{\rm 1.4}$
over different redshift ranges, out to z~4, and use X-ray stacking to calculate
the average s-BHAR in each $L^{\rm AGN}_{\rm 1.4}$-$z$ bin. We find that the
average s-BHAR is independent of $L^{\rm AGN}_{\rm 1.4}$, at all redshifts.
However, we see a strong increase of s-BHAR with redshift, at fixed $L^{\rm
AGN}_{\rm 1.4}$. This trend resembles the strong increase in the fraction of
star-forming host galaxies (based on the $(NUV-r)$ / $(r-J)$ colours) with
redshift, at fixed $L^{\rm AGN}_{\rm 1.4}$. A possible explanation for this
similarity might imply a link between average AGN radiative power and
availability of cold gas supply within the host galaxy. This study corroborates
the idea that radio-selected AGN become more radiatively efficient towards
earlier epochs, independently of their radio power.
