Train on multi-domains, then fine-tune on specific domain
Generally speaking, training with a broad distribution of data and then fine tuning on a specific domain generally leads to better performance and faster training time.
There are techniques such as meta-learning, domain invariance using techniques (ex. Gradient Reversal) or minimizing distance between the mean domain feature space using Maximum Mean Discrepency metrics. You could also familiarize yourself with empirical risk minimization and develop an intuition grounded on experiments. You could also check out 'A theory of learning from different domains' by Ben-David et al.