  The anomalous magnetic moment of the tau lepton, a_tau = (g_tau - 2)/2, is a
sensitive probe of new physics but is extremely difficult to measure precisely
in contrast to electron and muon moments. The best experimental limits were set
by the DELPHI collaboration more than 15 years ago in studies of the ditau
production in the e+e -> e+e+tau+tau process. Ultra-peripheral collisions
(UPCs) of heavy ions at the LHC may provide a unique opportunity to improve the
a_tau constraints in the studies of Pb+Pb -> Pb+Pb+tau+tau process. We review
recent proposals to study ditau production via semi-leptonic tau decays in
Pb-Pb UPC with the available ATLAS and CMS data and discuss the feasibility to
explore this process down to low transverse momenta of decay leptons with the
ALICE and LHCb experiments.
