People automatically make inferences about other people's personality traits based on their facial features. This study aims to apply a sequential experimental design based on Bayesian optimization (BO) in order to elucidate the relationship between impressions of personality and faces and facial features. We used a BO that incorporates Gaussian process preference learning (GPPL) which allows us to estimate a utility function based on a pairwise comparison task. One hundred and six Japanese university students provided photographs and each male and female facial image was embedded into a latent representation (18 x 512 dimensions) in the StyleGAN2 network using the Flickr-Faces-HQ (FFHQ) dataset. Using PCA, the dimensions of the latent representations were reduced to an 8- dimensional subspace, which we refer to as the Japanese face space. The participants were asked to select which faces were more trustworthy from among the images in the first session and the more dominant faces in the second session. The stimulus images were synthesized using the pre-trained StyleGAN2 model within the face space. Each session consisted of 100 trials. The stimuli for each session of the first 95 trials were created based on randomly generated parameters in the face subspace, while the stimuli for the remaining five trials were created based on the parameters calculated using the acquisition function. Facial traits related to trustworthiness and dominance were estimated based on the averaged utility functions. The impression of trustworthiness was found to be associated with facial aversion, while dominance was associated with sexual dimorphism. The results suggest that GPPL is an effective method for elucidating average psychological evaluations of complex stimuli.