In face recognition, designing margin-based (e.g., angular, additive, additive angular margins) softmax loss functions plays an important role to learn discriminative features. However, these hand-crafted heuristic methods may be sub-optimal because they require much effort to explore the large design space. Recently, an AutoML for loss function search method AM-LFS has been derived, which leverages reinforcement learning to search loss functions during the training process. But its search space is complex and unstable that hindering its superiority. In this paper, we first analyze that the key to enhance the feature discrimination is actually how to reduce the softmax probability. We then design a unified formulation for the current margin-based softmax losses. Accordingly, we define a novel search space and develop a reward-guided search method to automatically obtain the best candidate. Experimental results on a variety of face recognition benchmarks have demonstrated the effectiveness of our method over the state-of-the-art alternatives.