  Diffuse interstellar bands (DIBs) are weak and broad interstellar absorption
features in astronomical spectra originating from unknown molecules. To measure
DIBs in spectra of late-type stars more accurately and more efficiently, we
developed a Random Forest model to isolate the DIB features from the stellar
components and applied this method to 780 thousand spectra collected by the
Gaia Radial Velocity Spectrometer (RVS) that were published in the third data
release (DR3). After subtracting the stellar components, we modeled the DIBs
$\lambda$8621 and $\lambda$8648. After quality control, we selected 7619
reliable measurements. The rest-frame wavelength of DIB $\lambda$8621 was
updated as $\lambda_0\,{=}\,8623.141\,{\pm}\,0.030$ AA in vacuum, corresponding
to 8620.766 AA in air, which was determined by 77 DIB measurements toward the
Galactic anti-center. With the peak finding method and a coarse analysis, DIB
$\lambda$8621 was found to correlate better with the neutral hydrogen than the
molecular hydrogen (represented by $^{12}$CO $J\,{=}\,(1{-}0)$ emission). We
also obtained 179 reliable measurements of DIB $\lambda$8648 in the RVS spectra
of individual stars for the first time, further confirming this very broad DIB
feature. A rough estimation of $\lambda_0$ for DIB $\lambda$8648 was 8646.31 AA
in vacuum, corresponding to 8643.93 AA in air, assuming that the carriers of
$\lambda$8621 and $\lambda$8648 are co-moving. We confirmed the impact of
stellar residuals on the DIB measurements in Gaia DR3, which led to a
distortion of the DIB profile and a shift of the center ($\lesssim0.5$ AA), but
the EW was consistent with our new measurements. With our measurements and
analyses, we propose that the machine-learning-based approach can be widely
applied to measure DIBs in numerous spectra from spectroscopic surveys.
