Unbiased Gradient Estimation for Distributionally Robust Learning

Seeking to improve model generalization, we consider a new approach based on distributionally robust learning (DRL) that applies stochastic gradient descent to the outer minimization problem. Our algorithm efficiently estimates the gradient of the inner maximization problem through multi-level Monte Carlo randomization. Leveraging theoretical results that shed light on why standard gradient estimators fail, we establish the optimal parameterization of the gradient estimators of our approach that balances a fundamental tradeoff between computation time and statistical variance. Numerical experiments demonstrate that our DRL approach yields significant benefits over previous work.

Efficient Stochastic Gradient Descent for Distributionally Robust Learning

We consider a new stochastic gradient descent algorithm for efficiently solving general min-max optimization problems that arise naturally in distributionally robust learning. By focusing on the entire dataset, current approaches do not scale well. We address this issue by initially focusing on a subset of the data and progressively increasing this support to statistically cover the entire dataset.