  We model learning in a continuous-time Brownian setting where there is prior
ambiguity. The associated model of preference values robustness and is
time-consistent. It is applied to study optimal learning when the choice
between actions can be postponed, at a per-unit-time cost, in order to observe
a signal that provides information about an unknown parameter. The
corresponding optimal stopping problem is solved in closed-form, with a focus
on two specific settings: Ellsberg's two-urn thought experiment expanded to
allow learning before the choice of bets, and a robust version of the classical
problem of sequential testing of two simple hypotheses about the unknown drift
of a Wiener process. In both cases, the link between robustness and the demand
for learning is studied.
