  [Abridged] We present a search for fast optical transients (~0.5 hr-1 day)
using repeated observations of the Pan-STARRS1 Medium-Deep Survey (PS1/MDS)
fields. Our search takes advantage of the consecutive g/r-band observations
(16.5 min in each filter), by requiring detections in both bands, with
non-detections on preceding and subsequent nights. We identify 19 transients
brighter than 22.5 AB mag (S/N>10). Of these, 11 events exhibit quiescent
counterparts in the deep PS1/MDS templates that we identify as M4-M9 dwarfs.
The remaining 8 transients exhibit a range of properties indicative of
main-belt asteroids near the stationary point of their orbits. With
identifications for all 19 transients, we place an upper limit of
R_FOT(0.5hr)<0.12 deg^-2 d^-1 (95% confidence level) on the sky-projected rate
of extragalactic fast transients at <22.5 mag, a factor of 30-50 times lower
than previous limits; the limit for a timescale of ~day is R_FOT<2.4e-3 deg^-2
d^-1. To convert these sky-projected rates to volumetric rates, we explore the
expected peak luminosities of fast optical transients powered by various
mechanisms, and find that non-relativistic events are limited to M~-10 mag
(M~-14 mag) for a timescale of ~0.5 hr (~day), while relativistic sources
(e.g., GRBs, magnetar-powered transients) can reach much larger luminosities.
The resulting volumetric rates are <13 (M~-10 mag), <0.05 (M~-14 mag) and <1e-6
Mpc^-3 yr^-1 (M~-24 mag), significantly above the nova, supernova, and GRB
rates, respectively, indicating that much larger surveys are required to
provide meaningful constraints. Motivated by the results of our search we
discuss strategies for identifying fast optical transients in the LSST main
survey, and reach the optimistic conclusion that the veil of foreground
contaminants can be lifted with the survey data, without the need for expensive
follow-up observations.
