Modern machine learning pipelines are increasingly combining and mixing data from diverse and disparate sources, e.g., pre-training large language models. Yet, finding the optimal data mixture is a challenging and open problem. We formalize this data mixing problem as a bi-level objective: the best mixture is the one that would lead to the best model for a downstream objective. Unfortunately, this objective is generally intractable. In this paper, we make the observation that the bi-level data mixing objective bec…