  We have initiated a new survey for local extremely metal-poor galaxies
(EMPGs) with Subaru/Hyper Suprime-Cam (HSC) large-area (~500 deg^2) optical
images reaching a 5 sigma limit of ~26 magnitude, about 100 times deeper than
the Sloan Digital Sky Survey (SDSS). To select Z/Z_sun<0.1 EMPGs from ~40
million sources detected in the Subaru images, we first develop a
machine-learning (ML) classifier based on a deep neural network algorithm with
a training data set consisting of optical photometry of galaxy, star, and QSO
models. We test our ML classifier with SDSS objects having spectroscopic
metallicity measurements, and confirm that our ML classifier accomplishes
86%-completeness and 46%-purity EMPG classifications with photometric data.
Applying our ML classifier to the photometric data of the Subaru sources as
well as faint SDSS objects with no spectroscopic data, we obtain 27 and 86 EMPG
candidates from the Subaru and SDSS photometric data, respectively. We conduct
optical follow-up spectroscopy for 10 out of our EMPG candidates with
Magellan/LDSS-3+MagE, Keck/DEIMOS, and Subaru/FOCAS, and find that the 10 EMPG
candidates are star-forming galaxies at z=0.007-0.03 with large H_beta
equivalent widths of 104-265 A, stellar masses of log(M*/M_sun)=5.0-7.1, and
high specific star-formation rates of ~300 Gyr^{-1}, which are similar to those
of early galaxies at z>6 reported recently. We spectroscopically confirm that 3
out of 10 candidates are truly EMPGs with Z/Z_sun<0.1, one of which is HSC
J1631+4426, the most metal-poor galaxy with Z/Z_sun=0.016 reported ever.
