  One of the big challenges in machine learning applications is that training
data can be different from the real-world data faced by the algorithm. In
language modeling, users' language (e.g. in private messaging) could change in
a year and be completely different from what we observe in publicly available
data. At the same time, public data can be used for obtaining general knowledge
(i.e. general model of English). We study approaches to distributed fine-tuning
of a general model on user private data with the additional requirements of
maintaining the quality on the general data and minimization of communication
costs. We propose a novel technique that significantly improves prediction
quality on users' language compared to a general model and outperforms gradient
compression methods in terms of communication efficiency. The proposed
procedure is fast and leads to an almost 70% perplexity reduction and 8.7
percentage point improvement in keystroke saving rate on informal English
texts. We also show that the range of tasks our approach is applicable to is
not limited by language modeling only. Finally, we propose an experimental
framework for evaluating differential privacy of distributed training of
language models and show that our approach has good privacy guarantees.
