  We report on the search for optical counterparts to IceCube neutrino alerts
released between April 2016 and August 2021 with the All-Sky Automated Survey
for SuperNovae (ASAS-SN). Despite the discovery of a diffuse astrophysical
high-energy neutrino flux in 2013, the source of those neutrinos remains
largely unknown. Since 2016, IceCube has published likely-astrophysical
neutrinos as public realtime alerts. Through a combination of normal survey and
triggered target-of-opportunity observations, ASAS-SN obtained images within 1
hour of the neutrino detection for 20% (11) of all observable IceCube alerts
and within one day for another 57% (32). For all observable alerts, we obtained
images within at least two weeks from the neutrino alert. ASAS-SN provides the
only optical follow-up for about 17% of IceCube's neutrino alerts. We recover
the two previously claimed counterparts to neutrino alerts, the flaring-blazar
TXS 0506+056 and the tidal disruption event AT2019dsg. We investigate the light
curves of previously-detected transients in the alert footprints, but do not
identify any further candidate neutrino sources. We also analysed the optical
light curves of Fermi 4FGL sources coincident with high-energy neutrino alerts,
but do not identify any contemporaneous flaring activity. Finally, we derive
constraints on the luminosity functions of neutrino sources for a range of
assumed evolution models.
