The optical luminosity function of LOFAR radio-selected quasars at
  $1.4\leq z\leq5.0$ in the NDWFS-Bo\"otes field
  We present an estimate of the optical luminosity function (OLF) of LOFAR
radio-selected quasars (RSQs) at $1.4<z<5.0$ in the $9.3\:\textrm{deg}^{2}$
NOAO Deep Wide-field survey (NDWFS) of the Bo\"otes field. The selection was
based on optical/mid-ir photometry used to train three different machine
learning (ML) algorithms. Objects taken as quasars by the ML algorithms are
required to be detected at $5\sigma$ significance in deep radio maps to be
classified as candidate quasars. The optical imaging came from the SDSS and the
PS1 $3\pi$ survey; mid-ir photometry was taken from the SDWFS survey; and radio
data was obtained from deep LOFAR imaging of the NDWFS-Bo\"otes field. The
requirement of a $5\sigma$ LOFAR detection allowed us to reduce the stellar
contamination in our sample by two orders of magnitude. The sample comprises
134 objects, including both photometrically selected candidate quasars (47) and
spectroscopically confirmed quasars (83). The depth of our LOFAR observations
allowed us to detect the radio-emission of quasars that would be otherwise
classified as radio-quiet. Around $65\%$ of the quasars in the sample are
fainter than $M_{\textrm{1450}}=-24.0$, a regime where the OLF of quasars
selected through their radio emission, has not been investigated in detail. It
has been demonstrated that in cases where mid-ir wedge-based AGN selection is
not possible due to a lack of appropriate data, the selection of quasars using
ML algorithms trained with optical/mid-ir photometry in combination with LOFAR
data provides an excellent approach for obtaining samples of quasars. We
demonstrate that RSQs show an evolution similar to that exhibited by faint
quasars $(M_{\textrm{1450}}\leq-22.0)$. Finally, we find that RSQs may compose
up to $\sim20\%$ of the whole faint quasar population (radio-detected plus
radio-undetected).
