Recently, pre-training methods have shown remarkable success in task-oriented dialog (TOD) systems. However, most existing pretrained models for TOD focus on either dialog understanding or dialog generation, but not both. In this paper, we propose SPACE-3, a novel unified semi-supervised pre-trained conversation model learning from large-scale dialog corpora with limited annotations, which can be effectively fine-tuned on a wide range of downstream dialog tasks. Specifically, SPACE-3 consists of four successive components in a single transformer to maintain a task-flow in TOD systems: (i) a dialog encoding module to encode dialog history, (ii) a dialog understanding module to extract semantic vectors from either user queries or system responses, (iii) a dialog policy module to generate a policy vector that contains high-level semantics of the response, and (iv) a dialog generation module to produce appropriate responses. We design a dedicated pre-training objective for each component. Concretely, we pre-train the dialog encoding module with span mask language modeling to learn contextualized dialog information. To capture the structured dialog semantics, we pre-train the dialog understanding module via a novel tree-induced semi-supervised contrastive learning objective with the help of extra dialog annotations. In addition, we pre-train the dialog policy module by minimizing the L 2 distance between its output policy * Equal Contribution.† Wanwei He is also with the University of Chinese Academy of Sciences. This work was conducted when Wanwei He was interning at Alibaba.