  First results are presented from kinetic numerical simulations of
relativistic collisionless magnetic reconnection in pair plasma that include
radiation reaction from both synchrotron and inverse Compton (IC) processes,
motivated by non-thermal high-energy astrophysical sources, including in
particular blazars. These simulations are initiated from a configuration known
as 'ABC fields' that evolves due to coalescence instability and generates thin
current layers in its linear phase. Global radiative efficiencies, instability
growth rates, time-dependent radiation spectra, lightcurves, variability
statistics and the structure of current layers are investigated for a broad
range of initial parameters. We find that the IC radiative signatures are
generally similar to the synchrotron signatures. The luminosity ratio of IC to
synchrotron spectral components, the Compton dominance, can be modified by more
than one order of magnitude with respect to its nominal value. For very short
cooling lengths, we find evidence for modification of the temperature profile
across the current layers, no systematic compression of plasma density, and
very consistent profiles of E.B. We decompose the profiles of E.B with the use
of the Vlasov momentum equation, demonstrating a contribution from radiation
reaction at the thickness scale consistent with the temperature profile.
