  We present the results of a search for short-duration gravitational-wave
transients in the data from the second observing run of Advanced LIGO and
Advanced Virgo. We search for gravitational-wave transients with a duration of
milliseconds to approximately one second in the 32-4096 Hz frequency band with
minimal assumptions about the signal properties, thus targeting a wide variety
of sources. We also perform a matched-filter search for gravitational-wave
transients from cosmic string cusps for which the waveform is well-modeled. The
unmodeled search detected gravitational waves from several binary black hole
mergers which have been identified by previous analyses. No other significant
events have been found by either the unmodeled search or the cosmic string
search. We thus present search sensitivity for a variety of signal waveforms
and report upper limits on the source rate-density as function of the
characteristic frequency of the signal. These upper limits are a factor of
three lower than the first observing run, with a $50\%$ detection probability
for gravitational-wave emissions with energies of $\sim10^{-9}M_\odot c^2$ at
153 Hz. For the search dedicated to cosmic string cusps we consider several
loop distribution models, and present updated constraints from the same search
done in the first observing run.
