  We prove that any polar action on a separable Hilbert space by a connected
Hilbert Lie group does not have exceptional orbits. This generalizes a result
of Berndt, Console and Olmos in the finite dimensional Euclidean case. As an
application, we give a simple geometric proof of the fact that any hyperpolar
action on a simply connected compact Riemannian symmetric space by a connected
Lie group does not have exceptional orbits.
