Despite remarkable success in a variety of applications, it is well-known that deep learning can fail catastrophically when presented with out-of-distribution data. Toward addressing this challenge, we consider the domain generalization problem, wherein predictors are trained using data drawn from a family of related training domains and then evaluated on a distinct and unseen test domain. We show that under a natural model of data generation and a concomitant invariance condition, the domain generalization problem is equivalent to an infinite-dimensional constrained statistical learning problem; this problem forms the basis of our approach, which we call Model-Based Domain Generalization. Due to the inherent challenges in solving constrained optimization problems in deep learning, we exploit nonconvex duality theory to develop unconstrained relaxations of this statistical problem with tight bounds on the duality gap. Based on this theoretical motivation, we propose a novel domain generalization algorithm with convergence guarantees. In our experiments, we report improvements of up to 30 percentage points over state-of-the-art domain generalization baselines on several benchmarks including ColoredMNIST, Camelyon17-WILDS, FMoW-WILDS, and PACS.

翻译：尽管在各种应用中取得了显著的成功,但众所周知,如果提供分配外的数据,深层次的学习会灾难性地失败。为了应对这一挑战,我们考虑了领域普遍化问题,即利用来自相关培训领域大家庭的数据对预测人员进行培训,然后对不同和看不见的测试领域进行评估。我们表明,在数据生成的自然模型和伴随的不易变化条件下,广化问题相当于一个无限的统计学习限制问题;这个问题构成了我们方法的基础,我们称之为基于模型的通用化。由于在深层学习中解决有限优化问题的内在挑战,我们利用非编码的双重理论来发展这一统计问题不受限制的放松,同时对双重性差距进行严格限制。基于这一理论动机,我们提出了具有趋同保证的新版域化算法。我们在实验中报告,在包括有色的MNIST、Camelyon17-WILDS、FMoW-WLDS和PACS在内的若干基准方面,在最新版域通用基准方面改进了多达30个百分点。