Finding Optimally Robust Data Mixtures via Concave Maximization

Training on mixtures of data distributions is now common in many modern machine learning pipelines, useful for performing well on several downstream tasks. Group distributionally robust optimization (group DRO) is one popular way to learn mixture weights for training a specific model class, but group DRO methods suffer for non-linear models due to non-convex loss functions and when the models are non-parametric. We address these challenges by proposing to solve a more general DRO problem, giving a method we call MixMax. MixMax selects mixture weights by maximizing a particular concave objective with entropic mirror ascent, and, crucially, we prove that optimally fitting this mixture distribution over the set of bounded predictors returns a group DRO optimal model. Experimentally, we tested MixMax on a sequence modeling task with transformers and on a variety of non-parametric learning problems. In all instances MixMax matched or outperformed the standard data mixing and group DRO baselines, and in particular, MixMax improved the performance of XGBoost over the only baseline, data balancing, for variations of the ACSIncome and CelebA annotations datasets.