Periocular biometric covering the immediate vicinity of human eye is a synergistic alternative to face particularly when the face is masked or occluded. Most present work for periocular recognition in the wild are mainly convolutional neural networks learned based on cross-entropy loss. However, periocular images only capture the least salient face features, and thus suffering from severe intra-class compactness and inter-class dispersion issues for discriminative deep feature learning. Recently, label smoothing regularization (LSR) is discerned capable of diminishing the intra-class variation by minimizing the Kullback-Liebler divergence of a uniform distribution and a network prediction distribution. In this letter, we extend LSR to that of Generalized LSR (GLSR) by learning a pre-task network prediction, in place of the predefined uniform distribution. Extensive experiments on four periocular in the wild datasets disclose that the GSLR-trained networks prevail over the LSR-based counterpart and other most recent the state of the arts. This is supported by our empirical analyses that the embedding periocular features rendered by GLSR results in better class-wise cluster separation than the conventional LSR.