How to Calculate semantic similarity between video captions?
There's not exactly best solution, mostly depending on the experiment results. So maybe you need to try several different approaches to find out the best way. But one common way (to my knowledge) is using a word embedding (add an embedding layer or use GloVe, BERT etc.) to get the word vector, and then concatenate the word vectors in each sentence into sentence representation. You can calculate the similarity between the sentence representation.   

Well actually I don't practically test this :p, but I have read it in the papers. Therefore this approach is for reference only.