Searching in texts is still an open challenge. One of the viable approaches to fast and practical text browsing is similarity searching -- we can define a similarity function that determines the similarity between each pair of words, sentences or even whole documents. In 2018, a paper called The Case for Learned Index Structures has been published, arguing for a new paradigm for organizing and searching within complex data using machine learning. The goal of this thesis is to apply such an approach to the problem of similarity searching in text data and evaluate the results. Firstly, the student will have to get familiar with a great variety of approaches to text similarity, both lexical and semantic. Second, he will process these approaches for machine learning. Next, the text data will need to be indexed using an existing framework called Learned Metric Index (LMI) -- since the framework has never been used with this type of data, it will be necessary to identify the distinctive characteristics of text data and modify the setup of LMI to appropriately represent similarity within the text datasets. Finally, the searching efficiency of the resulting index will be evaluated experimentally.