Minimax Regret Optimization for Robust Machine Learning under Distribution Shift
This addresses the challenge of robust model performance in real-world scenarios with distribution shifts, offering a potential improvement over current methods, though it appears incremental as it builds on existing robust optimization frameworks.
The paper tackles the problem of ensuring uniformly low regret for machine learning models under unknown distribution shifts, showing that Distributionally Robust Optimization fails to guarantee this and proposing Minimax Regret Optimization as an alternative that achieves uniformly low regret under suitable conditions.
In this paper, we consider learning scenarios where the learned model is evaluated under an unknown test distribution which potentially differs from the training distribution (i.e. distribution shift). The learner has access to a family of weight functions such that the test distribution is a reweighting of the training distribution under one of these functions, a setting typically studied under the name of Distributionally Robust Optimization (DRO). We consider the problem of deriving regret bounds in the classical learning theory setting, and require that the resulting regret bounds hold uniformly for all potential test distributions. We show that the DRO formulation does not guarantee uniformly small regret under distribution shift. We instead propose an alternative method called Minimax Regret Optimization (MRO), and show that under suitable conditions this method achieves uniformly low regret across all test distributions. We also adapt our technique to have stronger guarantees when the test distributions are heterogeneous in their similarity to the training data. Given the widespead optimization of worst case risks in current approaches to robust machine learning, we believe that MRO can be a strong alternative to address distribution shift scenarios.