  Despite their empirical success, most existing listwiselearning-to-rank (LTR)
models are not built to be robust to errors in labeling or annotation,
distributional data shift, or adversarial data perturbations. To fill this gap,
we introduce a new listwise LTR model called Distributionally Robust
Multi-output Regression Ranking (DRMRR). Different from existing methods, the
scoring function of DRMRR was designed as a multivariate mapping from a feature
vector to a vector of deviation scores, which captures local context
information and cross-document interactions. DRMRR uses a Distributionally
Robust Optimization (DRO) framework to minimize a multi-output loss function
under the most adverse distributions in the neighborhood of the empirical data
distribution defined by a Wasserstein ball. We show that this is equivalent to
a regularized regression problem with a matrix norm regularizer. Our
experiments were conducted on two real-world applications, medical document
retrieval, and drug response prediction, showing that DRMRR notably outperforms
state-of-the-art LTR models. We also conducted a comprehensive analysis to
assess the resilience of DRMRR against various types of noise: Gaussian noise,
adversarial perturbations, and label poisoning. We show that DRMRR is not only
able to achieve significantly better performance than other baselines, but it
can maintain a relatively stable performance as more noise is added to the
data.
