Robust Learning in Heterogeneous Contexts

TL;DR

This paper introduces a robust learning method for data from diverse contexts with unknown distributions, balancing performance and robustness by considering statistical coverage and excess risks.

Contribution

It proposes a scalable approach that interpolates between empirical risk minimization and minimax regret, improving robustness without sacrificing nominal performance.

Findings

Effective in worst-case scenarios

Maintains performance in nominal conditions

Scalable to real and synthetic data

Abstract

We consider the problem of learning from training data obtained in different contexts, where the underlying context distribution is unknown and is estimated empirically. We develop a robust method that takes into account the uncertainty of the context distribution. Unlike the conventional and overly conservative minimax approach, we focus on excess risks and construct distribution sets with statistical coverage to achieve an appropriate trade-off between performance and robustness. The proposed method is computationally scalable and shown to interpolate between empirical risk minimization and minimax regret objectives. Using both real and synthetic data, we demonstrate its ability to provide robustness in worst-case scenarios without harming performance in the nominal scenario.