Title: Gradient Estimation for Unseen Domain Risk Minimization with Pre-Trained Models. Abstract: Domain generalization aims to build generalized models that perform well on unseen domains when only source domains are available for model optimization. Recent studies have demonstrated that large-scale pre-trained models could play an important role in domain generalization by providing their generalization power. However, large-scale pre-trained models are not fully equipped with target task-specific knowledge due to a discrepancy between the pre-training objective and the target task. Although the task-specific knowledge could be learned from source domains by fine-tuning, this hurts the generalization power of the pre-trained models because of gradient bias toward the source domains. To address this issue, we propose a new domain generalization method that estimates unobservable gradients that reduce potential risks in unseen domains, using a large-scale pre-trained model. Our proposed method allows the pre-trained model to learn task-specific knowledge further while preserving its generalization ability with the estimated gradients. Experimental results show that our proposed method outperforms baseline methods on DomainBed, a standard benchmark in domain generalization. We also provide extensive analyses to demonstrate that the estimated unobserved gradients relieve the gradient bias, and the pre-trained model learns the task-specific knowledge without sacrificing its generalization power.