  We have revisited the problem of metallicity prediction of RR Lyrae stars
from their near-infrared light curves in the Cousins I waveband. Our study is
based on high-quality time-series photometry and state-of-the-art
high-resolution spectroscopic abundance measurements of 80 fundamental-mode
(RRab) and 24 first-overtone (RRc) stars, spanning $\sim$[$-2.7$,$+0.18$] dex
and $\sim$[$-3$,$-0.5$] dex ranges, respectively. Employing machine-learning
methods, we investigated various light-curve representations and regression
models to identify their optimal form for our objective. Accurate new empirical
relations between the [Fe/H] iron abundance and the light-curve parameters have
been obtained using Bayesian regression for both RRab and RRc stars with mean
absolute prediction errors of 0.16 and 0.18 dex, respectively. We found that
earlier $I$-band [Fe/H] estimates had a systematic positive bias of up to $\sim
0.4$ dex in the metal-poor regime. Our new predictive models were deployed on
large ensembles of RR Lyrae stars to obtain photometric metallicity
distribution functions (MDFs) for various old stellar populations in and around
the Milky Way. We find that the mode of the old bulge component's MDF is
approximately $-1.4$ dex, in remarkable agreement with the latest spectroscopic
result. Furthermore, we derive MDF modes of $-1.83$, $-2.13$, and $-1.77$ dex
for the Large and Small Magellanic Clouds, and the Sagittarius dwarf galaxy,
respectively.
