  Radio-mode feedback is a key ingredient in galaxy formation and evolution
models, required to reproduce the observed properties of massive galaxies in
the local Universe. We study the cosmic evolution of radio-AGN feedback out to
$z\sim2.5$ using a sample of 9485 radio-excess AGN. We combine the evolving
radio luminosity functions with a radio luminosity scaling relationship to
estimate AGN jet kinetic powers and derive the cosmic evolution of the kinetic
luminosity density, $\Omega_{\rm{kin}}$ (i.e. the volume-averaged heating
output). Compared to all radio-AGN, low-excitation radio galaxies (LERGs)
dominate the feedback activity out to $z\sim2.5$, with both these populations
showing a constant heating output of $\Omega_{\rm{kin}} \approx 4-5 \times
10^{32}\,\rm{W\,Mpc^{-3}}$ across $0.5 < z < 2.5$. We compare our observations
to predictions from semi-analytical and hydrodynamical simulations, which
broadly match the observed evolution in $\Omega_{\rm{kin}}$, although their
absolute normalisation varies. Comparison to the Semi-Analytic Galaxy Evolution
(SAGE) model suggests that radio-AGN may provide sufficient heating to offset
radiative cooling losses, providing evidence for a self-regulated AGN feedback
cycle. We integrate the kinetic luminosity density across cosmic time to obtain
the kinetic energy density output from AGN jets throughout cosmic history to be
$\sim 10^{50}\,\rm{J\,Mpc^{-3}}$. Compared to AGN winds, the kinetic energy
density from AGN jets dominates the energy budget at $z \lesssim 2$; this
suggests that AGN jets play an important role in AGN feedback across most of
cosmic history.
