Paper:
MULTI-DOMAIN ADVERSARIAL LEARNING
Multi-domain learning (MDL) aims at obtaining a model with minimal average risk across multiple domains. Our empirical motivation is automated microscopy data, where cultured cells are imaged after being exposed to known and unknown chemical perturbations, and each dataset displays significant experimental bias. This paper presents a multi-domain adversarial learning approach, MULANN, to leverage multiple datasets with overlapping but distinct class sets, in a semisupervised setting. Our contributions include: i) a bound on the average-and worst-domain risk in MDL, obtained using the H-divergence; ii) a new loss to accommodate semi-supervised multi-domain learning and domain adaptation; iii) the experimental validation of the approach, improving on the state of the art on three standard image benchmarks, and a novel bioimage dataset, CELL.

Review:
Summary:
The manuscript proposes a multi-domain adversarial learning (MDL) method called MULANN, to leverage multiple datasets with overlapping but distinct class sets, in a semi-supervised setting. The authors define a new discrimination task to discriminate, within each domain, labeled samples from unlabeled ones that most likely belong to extra classes (classes with no labeled or unlabeled samples in the domain). They also introduce a bound on the average- and worst-domain risk in MDL, obtained using the H-divergence.
Strengths:
- The idea of using discriminators for separating the labeled samples from unlabeled ones that most likely belong to extra classes is interesting.
- A new generalization bound for MDL is introduced.
- The paper was clear, well written, well-motivated and nicely structured.
- The authors perform numerous empirical experiments on several types of problems on various datasets (Digit, OFFICE,CELL) successfully showing how the MULANN can reduce the nasty effects of the adversarial domain discriminator and repulse (a fraction of) unlabeled examples from labeled ones in each domain.
Weaknesses:
- all the experiments except the last row of Table 2 concern adaptation between two domains. Given the paper title, the reviewer would have expected more experiments in a multiple domain context. More precisely, for the digit datasets, the reviewer was interested to see how the proposed MDL performs on jointly adapting SVHN, MNIST, MNIST-M, and USPS or jointly adapting DSLR, Amazon, and Webcam for OFFICE dataset. Moreover, comparison with some of the DA baselines (ADDA[1], DSN[2]) is missing.
- The authors propose to rank the unlabeled samples of each domain according to the entropy of their classification of the current classifier. Obviously there must be some false ranking (specially at the initial stages of updating the classifier) for the unlabeled samples (e.g. the classifier may output high entropy for the unlabeled samples of the classes with labeled samples) and they may harm the performance of adaptation.  It is not clear how MULANN can work in this situation and how its performance vary with the noisy signals conveyed in those false pseudolabeled samples.
- Although the paper introduces the generalization bound for MDL, it does not give new formulation or algorithm to handle MDL (MULANN handles only the class asymmetry when domains involve distinct sets of classes and it has nothing to do with MDL). hence, there is no connection between the theoretical results on MDL generalization bound and the proposed method MULANN.
- Since each domain may have different number of classes, it is not clear how the number of classes (L) is set in the classification module (maximum number of classes in all domain?).
The reviewer is also interested to see how the the generalization bound introduced in this paper is related to the recent theoretical works [3],[4] on MDL.
[1] Tzeng, Eric, et al. "Adversarial discriminative domain adaptation." Computer Vision and Pattern Recognition (CVPR). Vol. 1. No. 2. 2017.
[2] Bousmalis, Konstantinos, et al. "Domain separation networks." Advances in Neural Information Processing Systems. 2016.
[3] Zhao, Han, et al. "Multiple Source Domain Adaptation with Adversarial Learning." Advances in Neural Information Processing Systems. 2018.
[4] Hoffman, Judy, Mehryar Mohri, and Ningshan Zhang. "Algorithms and Theory for Multiple-Source Adaptation."  Advances in Neural Information Processing Systems. 2018.