  We present the rest-1500\AA\ UV luminosity functions (LF) for star-forming
galaxies during the cosmic \textit{high noon} -- the peak of cosmic star
formation rate at $1.5<z<3$. We use deep NUV imaging data obtained as part of
the \textit{Hubble} Ultra-Violet Ultra Deep Field (UVUDF) program, along with
existing deep optical and NIR coverage on the HUDF. We select F225W, F275W and
F336W dropout samples using the Lyman break technique, along with samples in
the corresponding redshift ranges selected using photometric redshifts and
measure the rest-frame UV LF at $z\sim1.7,2.2,3.0$ respectively, using the
modified maximum likelihood estimator. We perform simulations to quantify the
survey and sample incompleteness for the UVUDF samples to correct the effective
volume calculations for the LF. We select galaxies down to
$M_{UV}=-15.9,-16.3,-16.8$ and fit a faint-end slope of
$\alpha=-1.20^{+0.10}_{-0.13}, -1.32^{+0.10}_{-0.14}, -1.39^{+0.08}_{-0.12}$ at
$1.4<z<1.9$, $1.8<z<2.6$, and $2.4<z<3.6$, respectively. We compare the star
formation properties of $z\sim2$ galaxies from these UV observations with
results from H\alpha\ and UV$+$IR observations. We find a lack of high SFR
sources in the UV LF compared to the H\alpha\ and UV$+$IR, likely due to dusty
SFGs not being properly accounted for by the generic $IRX-\beta$ relation used
to correct for dust. We compute a volume-averaged UV-to-H\alpha\ ratio by
\textit{abundance matching} the rest-frame UV LF and H\alpha\ LF. We find an
increasing UV-to-H\alpha\ ratio towards low mass galaxies ($M_\star \lesssim
5\times10^9$ M$_\odot$). We conclude that this could be due to a larger
contribution from starbursting galaxies compared to the high-mass end.
