Does Distributionally Robust Supervised Learning Give Robust Classifiers?

TL;DR

This paper critically analyzes Distributionally Robust Supervised Learning (DRSL) for classification, revealing its limitations in robustness due to inherent pessimism, and proposes a simple, more effective alternative.

Contribution

The paper provides a theoretical analysis of DRSL's limitations in classification and introduces a simple alternative method to improve robustness.

Findings

DRSL tends to fit the training distribution exactly, limiting robustness.

The pessimism in DRSL arises from the choice of loss functions and the broad distribution set.

Proposed simple DRSL method empirically outperforms standard DRSL in robustness.

Abstract

Distributionally Robust Supervised Learning (DRSL) is necessary for building reliable machine learning systems. When machine learning is deployed in the real world, its performance can be significantly degraded because test data may follow a different distribution from training data. DRSL with f-divergences explicitly considers the worst-case distribution shift by minimizing the adversarially reweighted training loss. In this paper, we analyze this DRSL, focusing on the classification scenario. Since the DRSL is explicitly formulated for a distribution shift scenario, we naturally expect it to give a robust classifier that can aggressively handle shifted distributions. However, surprisingly, we prove that the DRSL just ends up giving a classifier that exactly fits the given training distribution, which is too pessimistic. This pessimism comes from two sources: the particular losses used in classification and the fact that the variety of distributions to which the DRSL tries to be robust is too wide. Motivated by our analysis, we propose simple DRSL that overcomes this pessimism and empirically demonstrate its effectiveness.