The star formation rates and the stellar masses of the host galaxies of active galactic nuclei (AGNs) at high redshifts are key to understanding the evolution of the relation between the mass of the spheroidal component of a galaxy and the mass of its central black hole (Mbulge-M? relation). We investigate the host galaxies of 31 AGNs with spectroscopic redshifts between 2 and 4 found in the deep Chandra surveys of the Great Observatories Origins Deep Surveys (GOODS) fields. We use the F606W, F775W, and F850LP band images obtained with the Advanced Camera for Surveys on the Hubble Space Telescope (HST). The sample can be divided into 17 "extended" AGNs and 14 "compact" AGNs based on the concentration parameter defined as the difference between the aperture magnitudes with 007 and 025 diameter. We derive the upper limits of the UV luminosities of the host galaxies of the compact AGN sample and the upper and lower limits of the UV luminosities of the host galaxies of the extended AGN sample. These limits are consistent with the knee of the luminosity function of the Lyman break galaxies at z ~ 3, suggesting moderate star formation rates, 40 M☉ yr-1, in the host galaxies of the AGNs at 2 zsp 4 without correcting the dust extinction. By combining the limits of the UV luminosities with the observed K-band magnitudes for the extended AGNs, we derive the upper and lower limits of the stellar masses of their host galaxies. The derived upper limits on the stellar masses range from 1010 to 1012 M☉. The upper limits imply that the Mbulge-M? relation of the high-redshift AGNs is different from that of the galaxies in the nearby universe, or the average Eddington ratio of the high-redshift AGNs is higher than that of low-redshift AGNs with lower luminosity.
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