  We present a reduced-cost implementation of the state-averaged driven
similarity renormalization group (SA-DSRG) based on the frozen natural orbital
(FNO) approach. The natural orbitals (NOs) are obtained by diagonalizing the
one-body reduced density matrix from SA-DSRG second-order perturbation theory
(SA-DSRG-PT2). Subsequently, the virtual NOs with occupation numbers (ONs)
smaller than a user-defined threshold are excluded from the high-level electron
correlation treatment beyond SA-DSRG-PT2. An additive second-order correction
is applied to the SA-DSRG Hamiltonian to reintroduce the correlation effect
from the discarded orbitals. The FNO SA-DSRG method is benchmarked on 35 small
organic molecules in the QUEST database. When keeping 98-99% of the cumulative
ONs, the mean absolute error in the vertical transition energies due to FNO is
less than 0.01 eV. Using the same FNO threshold, we observe a speedup of 9
times the conventional SA-DSRG implementation for nickel carbonyl with a
quadruple-$\zeta$ basis set. The FNO approach enables third-order SA-DSRG
perturbation theory computations on chloroiron corrole
[FeCl(C$_{19}$H$_{11}$N$_4$)] with more than 1000 basis functions.
