We present the results of a machine-learning (ML)-based search for new R Coronae Borealis (RCB) stars and DY Persei-like stars (DYPers) in the Galaxy using cataloged light curves from the All-Sky Automated Survey (ASAS) Catalog of Variable Stars (ACVS). RCB stars—a rare class of hydrogen-deficient carbon-rich supergiants—are of great interest owing to the insights they can provide on the late stages of stellar evolution. DYPers are possibly the low-temperature, low- luminosity analogs to the RCB phenomenon, though additional examples are needed to fully establish this connection. While RCB stars and DYPers are traditionally identified by epochs of extreme dimming that occur without regularity, the ML search framework more fully captures the richness and diversity of their photometric behavior. We demonstrate that our ML method can use newly discovered RCB stars to identify additional candidates within the same data set. Our search yields 15 candidates that we consider likely RCB stars/DYPers: new spectroscopic observations confirm that four of these candidates are RCB stars and four are DYPers. Our discovery of four new DYPers increases the number of known Galactic DYPers from two to six; noteworthy is that one of the new DYPers has a measured parallax and is m ≈ 7 mag, making it the brightest known DYPer to date. Future observations of these new DYPers should prove instrumental in establishing the RCB connection. We consider these results, derived from a machine- learned probabilistic classification catalog, as an important proof-of-concept for the efficient discovery of rare sources with time-domain surveys.