On the Pareto Front of Multilingual Neural Machine Translation

In this work, we study how the generalization performance of a given direction changes with its sampling ratio in Multilingual Neural Machine Translation (MNMT). By training over 200 multilingual models with various model sizes, directions, and total numbers of tasks, we find that scalarization leads to a multitask trade-off front that deviates from the traditional Pareto front when there exists data imbalance in the training corpus. That is, the performance of certain translation directions does not improve with the increase of its weight in the multi-task optimization objective, which poses a great challenge to improve the overall performance of all directions. Based on our observations, we propose the Double Power Law to predict the unique performance trade-off front in MNMT, which is robust across various languages, data adequacy, and the number of tasks. Finally, we formulate the sample ratio selection problem in MNMT as an optimization problem based on the Double Power Law, which achieves better performance than temperature searching and gradient manipulation methods using up to half of the total training budget in our experiments.