Personalized dialogue agents (DAs) powered by large pre-trained language models (PLMs) often rely on explicit persona descriptions to maintain personality consistency. However, such descriptions may not always be available or may pose privacy concerns. To tackle this bottleneck, we introduce PersonaPKT, a lightweight transfer learning approach that can build persona-consistent dialogue models without explicit persona descriptions. By representing each persona as a continuous vector, PersonaPKT learns implicit persona-specific features directly from a small number of dialogue samples produced by the same persona, adding less than 0.1% trainable parameters for each persona on top of the PLM backbone. Empirical results demonstrate that PersonaPKT effectively builds personalized DAs with high storage efficiency, outperforming various baselines in terms of persona consistency while maintaining good response generation quality. In addition, it enhances privacy protection by avoiding explicit persona descriptions. Overall, PersonaPKT is an effective solution for creating personalized DAs that respect user privacy.