Xin Zou

Out-of-distribution (OOD) generalization has attracted increasing research attention in recent years, owing to its promising empirical results in real-world applications. However, theoretical studies on OOD generalization remain limited, particularly with respect to lower bounds on the generalization error. To better understand how source data contributes to improved OOD generalization performance, we take an initial step toward establishing a lower bound on the OOD generalization error, and subsequently investigate upper bounds from the perspective of statistical learning theory. Interestingly, we find that under some conditions, simply minimizing the average empirical risk over the source domains can yield a nearly optimal error rate (up to a logarithmic factor) without requiring knowledge or estimation of distributional parameters or the discrepancy between source and target domains. This finding offers an explanation for the surprising phenomenon observed in DomainBed, where carefully designed OOD generalization algorithms fail to outperform the simple empirical risk minimization (ERM) algorithm. Our results also imply a no-free-lunch theorem and provide an optimistic bound for OOD generalization.

AdaBoost is a well-known algorithm in boosting. Schapire and Singer propose, an extension of AdaBoost, named AdaBoost.MH, for multi-class classification problems. Kégl shows empirically that AdaBoost.MH works better when the classical one-against-all base classifiers are replaced by factorized base classifiers containing a binary classifier and a vote (or code) vector. However, the factorization makes it much more difficult to provide a convergence result for the factorized version of AdaBoost.MH. Then, Kégl raises an open problem in COLT 2014 to look for a convergence result for the factorized AdaBoost.MH. In this work, we resolve this open problem by presenting a convergence result for AdaBoost.MH with factorized multi-class classifiers.

Out-of-distribution (OOD) generalization has attracted increasing research attention in recent years, due to its promising experimental results in real-world applications. In this paper, we study the confidence set prediction problem in the OOD generalization setting. Split conformal prediction (SCP) is an efficient framework for handling the confidence set prediction problem. However, the validity of SCP requires the examples to be exchangeable, which is violated in the OOD setting. Empirically, we show that trivially applying SCP results in a failure to maintain the marginal coverage when the unseen target domain is different from the source domain. To address this issue, we develop a method for forming confident prediction sets in the OOD setting and theoretically prove the validity of our method. Finally, we conduct experiments on simulated data to empirically verify the correctness of our theory and the validity of our proposed method.

Out-of-distribution (OOD) generalization has attracted increasing research attention in recent years, due to its promising experimental results in real-world applications. Interestingly, we find that existing OOD generalization methods are vulnerable to adversarial attacks. This motivates us to study OOD adversarial robustness. We first present theoretical analyses of OOD adversarial robustness in two different complementary settings. Motivated by the theoretical results, we design two algorithms to improve the OOD adversarial robustness. Finally, we conduct experiments to validate the effectiveness of our proposed algorithms. Our code is available at https://github.com/ZouXinn/OOD-Adv.

Deep networks are well-known to be fragile to adversarial attacks, and adversarial training is one of the most popular methods used to train a robust model. To take advantage of unlabeled data, recent works have applied adversarial training to contrastive learning (Adversarial Contrastive Learning; ACL for short) and obtain promising robust performance. However, the theory of ACL is not well understood. To fill this gap, we leverage the Rademacher omplexity to analyze the generalization performance of ACL, with a particular focus on linear models and multi-layer neural networks under \ell_p attack (p≥1). Our theory shows that the average adversarial risk of the downstream tasks can be upper bounded by the adversarial unsupervised risk of the upstream task. The experimental results validate our theory.