https://github.com/ShiyuNee/Facet-Generation}
Due to the ambiguity and vagueness of a user query, it is essential to identify the query facets for the clarification of user intents. Existing work on query facet generation has achieved compelling performance by sequentially predicting the next facet given previously generated facets based on pre-trained language generation models such as BART. Given a query, there are mainly two types of training objectives to guide the facet generation models. One is to generate the default sequence of ground-truth facets, and the other is to enumerate all the permutations of ground-truth facets and use the sequence that has the minimum loss for model updates. The second is permutation-invariant while the first is not. In this paper, we aim to conduct a systematic comparative study of various types of training objectives, with different properties of not only whether it is permutation-invariant but also whether it conducts sequential prediction and whether it can control the count of output facets. To this end, we propose another three training objectives of different aforementioned properties. For comprehensive comparisons, besides the commonly used evaluation that measures the matching with ground-truth facets, we also introduce two diversity metrics to measure the diversity of the generated facets. Based on an open-domain query facet dataset, i.e., MIMICS, we conduct extensive analyses and show the pros and cons of each method, which could shed light on model training for clarification facet generation. The code can be found at \url{