We present rest-frame far-infrared (FIR) and optical size measurements of AGN hosts and star-forming galaxies in the COSMOS field, enabled by high-resolution ALMA/1 mm (0.1 arcsec - 0.4 arcsec) and HST/F814W imaging (~ 0.1 arcsec). Our sample includes 27 galaxies at z<2.5, classified as infrared-selected AGN (3 sources), X-ray selected AGN (4 sources), and non-AGN star-forming galaxies (20 sources), for which high-resolution Band 6/7 ALMA images are available at 1 mm from our own observing program as well as archival observations. The sizes and SFR surface densities measured from both ALMA/1 mm and HST/F814W images show that obscured AGN host galaxies are more compact than non-AGN star-forming galaxies at similar redshift and stellar mass. This result suggests that the obscured accretion phase may be related to galaxies experiencing a compaction of their gaseous component, which could be associated with enhanced central star formation before a subsequent quenching driving the formation of compact passive galaxies. Moreover, most of the detected and stacked rest-frame FIR sizes of AGNs in our sample are similar or more compact than their rest-frame optical sizes, which is consistent with recent results of ALMA detected sources. This might be explained by the fact that the dusty starbursts take place in the compact regions, and suggests that the star formation mechanisms in the compact regions of AGN hosts are similar to those observed in star-forming galaxies observed with ALMA.
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