  We propose a novel scenario for possible electromagnetic (EM) emission by
compact binary mergers in the accretion disks of active galactic nuclei (AGNs).
Nuclear star clusters in AGNs are a plausible formation site of compact-stellar
binaries (CSBs) whose coalescences can be detected through gravitational waves
(GWs). We investigate the accretion onto and outflows from CSBs embedded in AGN
disks. We show that these outflows are likely to create outflow "cavities" in
the AGN disks before the binaries merge, which makes EM or neutrino
counterparts much less common than would otherwise be expected. We discuss the
necessary conditions for detectable EM counterparts to mergers inside the
outflow cavities. If the merger remnant black hole experiences a high recoil
velocity and can enter the AGN disk, it can accrete gas with a super-Eddington
rate, newly forming a cavity-like structure. This bubble can break out of the
disk within a day to a week after the merger. Such breakout emission can be
bright enough to be detectable by current soft X-ray instruments, such as {\it
Swift}-XRT and {\it Chandra}.
