  Binary black hole mergers encode information about their environment and the
astrophysical processes that led to their formation. Measuring the redshift
dependence of their merger rate will help probe the formation and evolution of
galaxies and the evolution of the star formation rate. Here we compute the
cosmic evolution of the merger rate for stellar-mass binaries in the disks of
Active Galactic Nuclei (AGNs). We focus on recent evolution out to redshift
$z=2$, covering the accessible range of current Earth-based gravitational-wave
observatories. On this scale, the AGN population density is the main
contributor to redshift-dependence. We find that the AGN-assisted merger rate
does not meaningfully evolve with redshift, differentiating this channel from
field binaries and some other dynamical formation scenarios.
