  We introduce $\mathbb Z_2$-valued bulk invariants for symmetry-protected
topological phases in $2+1$ dimensional driven quantum systems. These
invariants adapt the $W_3$-invariant, expressed as a sum over degeneracy points
of the propagator, to the respective symmetry class of the Floquet-Bloch
Hamiltonian. The bulk-boundary correspondence that holds for each invariant
relates a non-zero value of the bulk invariant to the existence of
symmetry-protected topological boundary states. To demonstrate this
correspondence we apply our invariants to a chiral Harper, time-reversal
Kane-Mele, and particle-hole symmetric graphene model with periodic driving,
where they successfully predict the appearance of boundary states that exist
despite the trivial topological character of the Floquet bands. Especially for
particle-hole symmetry, combination of the $W_3$ and the $\mathbb
Z_2$-invariants allows us to distinguish between weak and strong topological
phases.
