We discuss the flavor asymmetry of polarized light antiquarks in the nucleon, $\Delta\bar{u}-\Delta\bar{d}$. We present a determination of this quantity based on two global QCD analyses of experimental data, DSSV08 and NNPDFpol1.1, in which sea-quark parton distribution functions are determined respectively either from semi-inclusive deep-inelastic scattering or W-boson production data. The latter have become available only very recently, and their effect on the polarized flavor asymmetry is presented here for the first time. We find that the flavor asymmetry of polarized antiquarks in the nucleon is definitely positive, and has almost the same absolute size as its unpolarized counterpart. We compare this result with various theoretical models of the nucleon structure in order to test their validity. We show that some of them are clearly disfavored.