  Almost every known low-luminosity Milky Way dwarf spheroidal (dSph) satellite
galaxy contains at least one RR Lyrae star. Assuming that a fraction of distant
(60 < d_{helio} < 100 kpc) Galactic halo RR Lyrae stars are members of yet to
be discovered low-luminosity dSph galaxies, we perform a {\em guided} search
for these low-luminosity dSph galaxies. In order to detect the presence of dSph
galaxies, we combine stars selected from more than 123 sightlines centered on
RR Lyrae stars identified by the Palomar Transient Factory. We find that this
method is sensitive enough to detect the presence of Segue 1-like galaxies
(M_V= -1.5^{+0.6}_{-0.8}, r_h=30 pc) even if only ~20 sightlines were occupied
by such dSph galaxies. Yet, when our method is applied to the SDSS DR10 imaging
catalog, no signal is detected. An application of our method to sightlines
occupied by pairs of close (<200 pc) horizontal branch stars, also did not
yield a detection. Thus, we place upper limits on the number of low-luminosity
dSph galaxies with half-light radii from 30 pc to 120 pc, and in the probed
volume of the halo. Stronger constraints on the luminosity function may be
obtained by applying our method to sightlines centered on RR Lyrae stars
selected from the Pan-STARRS1 survey, and eventually, from LSST. In the
Appendix, we present spectroscopic observations of an RRab star in the
Bo\"{o}tes 3 dSph and a light curve of an RRab star near the Bo\"{o}tes 2 dSph.
