Abstract: When training multilingual machine translation (MT) models that can translate to/from multiple languages, we are faced with imbalanced training sets: some languages have much more training data than others. Standard practice is to up-sample less resourced languages to increase representation, and the degree of up-sampling has a large effect on the overall performance. In this paper, we propose a method that instead automatically learns how to weight training data through a data scorer that is optimized to maximize performance on all test languages. Experiments on two sets of languages under both one-to-many and many-to-one MT settings show our method not only consistently outperforms heuristic baselines in terms of average performance, but also offers flexible control over the performance of which languages are optimized.