A Challenge in Reweighting Data with Bilevel Optimization
This addresses a challenge in machine learning for practitioners dealing with distribution shifts between training and testing data.
The paper identifies that joint optimization of model parameters and data weights in bilevel data reweighting leads to sub-optimal, sparse weight solutions, explaining its limited practical use.
In many scenarios, one uses a large training set to train a model with the goal of performing well on a smaller testing set with a different distribution. Learning a weight for each data point of the training set is an appealing solution, as it ideally allows one to automatically learn the importance of each training point for generalization on the testing set. This task is usually formalized as a bilevel optimization problem. Classical bilevel solvers are based on a warm-start strategy where both the parameters of the models and the data weights are learned at the same time. We show that this joint dynamic may lead to sub-optimal solutions, for which the final data weights are very sparse. This finding illustrates the difficulty of data reweighting and offers a clue as to why this method is rarely used in practice.