  We present accurate results for optical conductivity of the three dimensional
Frohlich polaron in all coupling regimes. The systematic-error free
diagrammatic quantum Monte Carlo method is employed where the Feynman graphs
for the momentum-momentum correlation function in imaginary time are summed up.
The real-frequency optical conductivity is obtained by the analytic
continuation with stochastic optimization. We compare numerical data with
available perturbative and non-perturbative approaches to the optical
conductivity and show that the picture of sharp resonances due to relaxed
excited states in the strong coupling regime is ``washed out''by large
broadening of these states. As a result, the spectrum contains only a
single-maximum broad peak with peculiar shape and a shoulder.
