Out-of-distribution Robust Optimization

TL;DR

This paper addresses out-of-distribution robust optimization by proposing methods that leverage density ratio estimation and covariate structures to improve robustness against distribution shifts, demonstrated through numerical experiments.

Contribution

It introduces novel methods for out-of-distribution robust optimization that utilize density ratio estimation and covariate information, advancing beyond traditional in-distribution approaches.

Findings

Methods effectively handle distribution shifts.

Covariate and label shifts are crucial for robustness.

Proposed techniques reduce over-conservativeness in solutions.

Abstract

In this paper, we consider the contextual robust optimization problem under an out-of-distribution setting. The contextual robust optimization problem considers a risk-sensitive objective function for an optimization problem with the presence of a context vector (also known as covariates or side information) capturing related information. While the existing works mainly consider the in-distribution setting, and the resultant robustness achieved is in an out-of-sample sense, our paper studies an out-of-distribution setting where there can be a difference between the test environment and the training environment where the data are collected. We propose methods that handle this out-of-distribution setting, and the key relies on a density ratio estimation for the distribution shift. We show that additional structures such as covariate shift and label shift are not only helpful in defending distribution shift but also necessary in avoiding non-trivial solutions compared to other principled methods such as distributionally robust optimization. We also illustrate how the covariates can be useful in this procedure. Numerical experiments generate more intuitions and demonstrate that the proposed methods can help avoid over-conservative solutions.