  Due to the poor generalization performance of traditional empirical risk
minimization (ERM) in the case of distributional shift, Out-of-Distribution
(OoD) generalization algorithms receive increasing attention. However, OoD
generalization algorithms overlook the great variance in the quality of
training data, which significantly compromises the accuracy of these methods.
In this paper, we theoretically reveal the relationship between training data
quality and algorithm performance and analyze the optimal regularization scheme
for Lipschitz regularized invariant risk minimization. A novel algorithm is
proposed based on the theoretical results to alleviate the influence of
low-quality data at both the sample level and the domain level. The experiments
on both the regression and classification benchmarks validate the effectiveness
of our method with statistical significance.
