To obtain extensive annotated data for under-resourced languages is challenging, so in this research, we have investigated whether it is beneficial to train models using multi-task learning. Sentiment analysis and offensive language identification share similar discourse properties. The selection of these tasks is motivated by the lack of large labelled data for user-generated code-mixed datasets. This paper works on code-mixed YouTube comments for Tamil, Malayalam, and Kannada languages. Our framework is applicable to other sequence classification problems irrespective of the size of the datasets. Experiments show that our multi-task learning model can achieve high results compared with single-task learning while reducing the time and space constraints required to train the models on individual tasks. Analysis of fine-tuned models indicates the preference of multi-task learning over single-task learning resulting in a higher weighted F1-score on all three languages. We apply two multi-task learning approaches to three Dravidian languages: Kannada, Malayalam, and Tamil. Maximum scores on Kannada and Malayalam were achieved by mBERT subjected to cross-entropy loss and with an approach of hard parameter sharing. Best scores on Tamil was achieved by DistilBERT subjected to cross-entropy loss with soft parameter sharing as the architecture type. For the tasks of sentiment analysis and offensive language identification, the best-performing model scored a weighted F1-score of (66.8% and 90.5%), (59% and 70%), and (62.1% and 75.3%) for Kannada, Malayalam, and Tamil on sentiment analysis and offensive language identification, respectively. The data and approaches discussed in this paper are published in Githubfootnote{href{https://github.com/SiddhanthHegde/Dravidian-MTL-Benchmarking}{Dravidian-MTL-Benchmarking}}.
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