Leveraging vast and continually updated knowledge from the Internet has been considered an important ability for a dialogue system. Therefore, the dialogue query generation task is proposed for generating search queries from dialogue histories, which will be submitted to a search engine for retrieving relevant websites on the Internet. In this regard, previous efforts were devoted to collecting conversations with annotated queries and training a query producer (QP) via standard supervised learning. However, these studies still face the challenges of data scarcity and domain adaptation. To address these issues, in this paper, we propose a semi-supervised learning framework -- SemiDQG, to improve model performance with unlabeled conversations. Based on the observation that the search query is typically related to the topic of dialogue response, we train a response-augmented query producer (RA) to provide rich and effective training signals for QP. We first apply a similarity-based query selection strategy to select high-quality RA-generated pseudo queries, which are used to construct pseudo instances for training QP and RA. Then, we adopt the REINFORCE algorithm to further enhance QP, with RA-provided rewards as fine-grained training signals. Experimental results and in-depth analysis of three benchmarks show the effectiveness of our framework in cross-domain and low-resource scenarios. Particularly, SemiDQG significantly surpasses ChatGPT and competitive baselines. Our code is available at \url{https://github.com/DeepLearnXMU/SemiDQG}.
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