Paper:
Published as a conference paper at ICLR 2018 GENERALIZING ACROSS DOMAINS VIA CROSS-GRADIENT TRAINING
We present CROSSGRAD, a method to use multi-domain training data to learn a classifier that generalizes to new domains. CROSSGRAD does not need an adaptation phase via labeled or unlabeled data, or domain features in the new domain. Most existing domain adaptation methods attempt to erase domain signals using techniques like domain adversarial training. In contrast, CROSSGRAD is free to use domain signals for predicting labels, if it can prevent overfitting on training domains. We conceptualize the task in a Bayesian setting, in which a sampling step is implemented as data augmentation, based on domain-guided perturbations of input instances. CROSSGRAD parallelly trains a label and a domain classifier on examples perturbed by loss gradients of each other's objectives. This enables us to directly perturb inputs, without separating and re-mixing domain signals while making various distributional assumptions. Empirical evaluation on three different applications where this setting is natural establishes that (1) domain-guided perturbation provides consistently better generalization to unseen domains, compared to generic instance perturbation methods, and that (2) data augmentation is a more stable and accurate method than domain adversarial training.

Review:
This paper proposed a domain generalization approach by domain-dependent data augmentation. The augmentation is guided by a network that is trained to classify a data point to different domains. Experiments on four datasets verify the effectiveness of the proposed approach. 
Strengths:
+ The proposed classification model is domain-dependent, as opposed to being domain-invariant. This is new and differs from most existing works on domain adaptation/generalization, to the best of my knowledge. 
+ The experiments show that the proposed method outperforms two baselines. However, more related approaches could be included to strengthen the experiments (see below for details).
Weaknesses:
- The paper studies domain generalization and yet fails to position it in the right literature. By a simple search of "domain generalization" using Google Scholar, I found several existing works on this problem and have listed some below. The authors may consider to include them in both the related works and the experiments. 
Questions: 
1. It is intuitive to directly define the data augmentation by x_i+Grad_x J_d. Why is it necessary to instead define it as the inverse transformation G^{-1}(g') and then go through the approximations to derive the final augmentation? 
2. Is the CrossGrad training necessary? What if one trains the network in two steps? Step 1: learn G using J_d and a regularization to avoid misclassification over the labels using the original data. Step 2: Learn the classification network (possibly different from G) by the domain-dependent augmentation.
Saeid Motiian, Marco Piccirilli, Donald A. Adjeroh, and Gianfranco Doretto. Unified deep supervised
domain adaptation and generalization. In IEEE International Conference on Computer
Vision (ICCV), 2017.
Muandet, K., Balduzzi, D. and Schölkopf, B., 2013. Domain generalization via invariant feature representation. In Proceedings of the 30th International Conference on Machine Learning (ICML-13) (pp. 10-18).
Xu, Z., Li, W., Niu, L. and Xu, D., 2014, September. Exploiting low-rank structure from latent domains for domain generalization. In European Conference on Computer Vision (pp. 628-643). Springer, Cham.
Ghifary, M., Bastiaan Kleijn, W., Zhang, M. and Balduzzi, D., 2015. Domain generalization for object recognition with multi-task autoencoders. In Proceedings of the IEEE international conference on computer vision (pp. 2551-2559).
Gan, C., Yang, T. and Gong, B., 2016. Learning attributes equals multi-source domain generalization. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (pp. 87-97).