We have a series of data which want to label part of each series. As we do not have any training data, we try using Active Learning as a solution. But, the problem is our classifier is something like RNN which needs a lot of data to be trained. Hence, we have a problem in converging fast to just label proportional small parts of unlabeled data. The question is "is there any article about this problem (Active Learning and some complex classifiers like RNN) or not?".

Or is there any alternative to approach this problem or not? (as data is a series of actions)

As I found this case backs to the sequence labeling. Sequence labeling has some classic solution such as conditional random fields (CRFs) and hidden Markov model (HMM). Also, have some solution in Active learning (AL) which use from algorihtms such as struct SVM ($\text{SVM}^{\text{strcut}}$) like this paper.

Also, some NLP solutions in active learning could help to solve these kind of problems such as this paper which is about active learning in named entity recognition (NER).

Besides, the combination of active learning with Deep networks such as CNN happens. For example, this paper explains more about the idea.

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