Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: This paper introduces an algorithm for invariant representation learning for domain adaptation, which builds on the existing work by MDD in order to effectively calculate the $D_{\mathcal{H}\Delta \mathcal{H}}$ divergence using the source domain classifier. 
main_review: The paper is clearly presented and plenty of relevant related work is cited. The paper provides a meaningful discussion on the drawbacks of MDD and addresses the problem by introducing a bi-level optimization approach. Furthermore, the paper provides training strategies to improve performance (such as taking advantage of a linear $h$, how to make use of pseudo-labels, and cache-augmented training). The empirical experiments are comprehensive and seem convincing. 

One thing that would improve the paper would be a discussion on how DANN [Ganin et al., 2016] estimate the $D_{\mathcal{H}\Delta \mathcal{H}}$ divergence using adversarial training, and why it is necessary to have equation (13) when the divergence was initially minimized using adversarial training. 
limitations_and_societal_impact: No limitations are discussed, and any inclusion of them in the paper would be welcome.
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: The paper proposes warping probability discrepancy measures towards the end tasks. To achieve this, the authors leveraged the pseudo-labels from the optimal predictor with a new bi-level optimization-based approach.
main_review: ### Originality

The proposed framework is designed upon maximum mean discrepancy (MMD) and contrastive domain discrepancy (CDD). However, the modification is technically sound and novel.

### Quality

In Table 2, ASAN is not the state-of-the-art method. [ref1] achieves 71.8% on Office-Home dataset.

In Table 3, ASAN is not state-of-the-art method. It is encouraged to include recent state-of-the-art methods, such as [ref2] and [ref3]. [ref2] achieves 90.3% and [ref3] achieves 90.2%.


### Clarity

The paper is well written and easy to follow. The highlighted words were also helpful for understanding equations.

### Significance

The experimental results of the proposed method are not significant. For example, [ref1] outperforms the proposed method by 1.0% on Office-Home and [ref2] outperforms the proposed method by 0.9%.

[ref1] Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation, ICML 2020.

[ref2] Unsupervised Domain Adaptation via Structured Prediction Based Selective Pseudo-Labeling, AAAI 2020.

[ref3] Discriminative Feature Alignment: Improving Transferability of Unsupervised Domain Adaptation by Gaussian-guided Latent Alignment, Pattern Recognition 2021.

limitations_and_societal_impact: Yes
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: The paper "Implicit Task-Driven Probability Discrepancy Measure for Unsupervised Domain Adaptation" proposes a probability discrepancy measure in the context of unsupervised domain adaptation while keeping the end goal, namely, minimizing the target domain risk, as part of the measure. The proposed measure, i-MDD, is based on a modification of the $\mathcal{H} \Delta \mathcal{H}$-divergence of Ben-David et al. (2010) and Marginal Disparity Discrepancy (MDD) of Zhang et al. (2019). The paper then discusses practical considerations like how to actually minimize the i-MDD, which is noted to be simplified due to the structure of i-MDD, and then finally discusses experiments.
main_review: This paper is a mixed bag, it starts great by clearly introducing the problem and the preliminaries, but then completely loses its momentum by muddling its presentation on the new proposed discrepancy measure, arguably the part without which I cannot recommend accepting this paper. Let me expound on this.

For someone well-versed with the jargon of domain adaptation, reading the first two sections, introduction and preliminaries, and some parts of other sections leaves the reader with a clear picture of the problem and the literature. I am not an expert in domain adaptation, and some phrases like "margin disparity discrepancy" (MDD) or "contrastive domain discrepancy" were new to me. However, I could still get a reasonably complete picture by reading the aforementioned parts of the paper or by going through some of the references cited. But this is where the good parts end, and the problems start.

The paper fails to motivate or justify its development of the proposed discrepancy measure, namely equations (11) and (12). After introducing two other relevant measures of discrepancy, $\mathcal{H} \Delta \mathcal{H}$-divergence and MDD, the paper tries to reconcile these two measures by changing the MDD to make it look like $\mathcal{H} \Delta \mathcal{H}$-divergence. I don't see the point of this exercise at all. Why is this "conflict of spirit", as the authors put it, undesirable? The whole point of minimisation over $h$ in MDD is to select for those $h \in \mathcal{H}$ that have low source domain risk. I understand that optimizing for MDD or $\mathcal{H} \Delta \mathcal{H}$-divergence isn't easy and this is where i-MDD shines, but to me this analysis of reconciliation seems forced. Next, the lines 136-143 feel disconnected. A formulation is proposed in equation (10) which intuitively seems to strike a balance between $\mathcal{H} \Delta \mathcal{H}$-divergence and MDD, but then it is changed to something very different just on the grounds that GEM doesn't work here? Finally, there's the issue of the formulation of MDD in equation (6). It doesn't seem to correspond to the one discussed in the referenced paper by Zhang et al. (2019). I would appreciate if the authors could help me see how their formulation in equation (6) relates to Definition 3.2 of Zhang et al. where they propose the MDD. Relatedly, the formulation of i-MDD seems exactly the Disparity Discrepancy (DD) discussed in Definition 3.1 of Zhang et al. except with an extra $\alpha \mathcal{R}(h^*;\tilde{P}_\phi)$ term and the fact that a specific $h$ is being used, namely $h^*$. This reinforces my point that all the reconciliation seems superfluous.

There are other issues of notation as well:

1. One line 94, it is stated that $P := \phi \\# S$ and $\tilde{P} := \phi \\# \tilde{S}$. Did the authors intend $P := \phi \\# S_x$ and $\tilde{P} := \phi \\# \tilde{S}_x$ because otherwise it doesn't make sense. The feature extractor $\phi$ maps $\mathcal{X}$ to some latent space and $S$ is a distribution on $\mathcal{X} \times \mathcal{Y}$, and so $S \circ \phi^{-1}$ does not make sense.
2. What is $Q$ on line 100? Is it $\phi \\# T_x$?
3. On line 83, instead of $\tilde{T}$ did you intend $\tilde{T}_x$?

I did not check the experimental results.
limitations_and_societal_impact: N/A
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: In this paper, the authors propose a new bi-level optimization-based approach to handle the issue of [23], i.e., the proposed margin disparity discrepancy (MDD) measure conflicts with the H\DeltaH-divergence. The theoretical results are then applied to MDD and CDD, which gives the implicit task-driven discrepancy method, i-MDD and i-CDD. Experimental studies are done to verify the effectiveness of the proposed i-MDD and i-CDD.
main_review: Here are some comments:

Pros:
(1)	The paper is well-written and easy to follow. 

(2)	The theoretical analyses are given to motivate the implicit task-driven disparity discrepancy.

(3)	New implicit task-driven MDD and CDD, i.e., i-MDD and i-CDD, are given.

Cons:

(1)	The paper needs a thorough related work section to elaborate the existing domain adaptation learning theory as well as the corresponding domain adaptation algorithms. Discussions on how the current work differentiates from existing works are needed. 

(2)	Regarding Eq. (4), it is necessary to provide more details on how this equation relates to what equation of [16].

(3)	The proposed two method i-CDD and i-MDD are not well compared, e.g., pros and cons. Moreover, is there any guide on which one should be used in what scenario?

(4)	The empirical results of i-CDD and i-MDD are only comparable with the state-of-the-art methods (in each dataset, we can find some comparable baselines), which makes the methods less convincing.

(5)	Figure 3 shows that the cache size is an important factor affecting the final performance. Is there any rule to set such a hyper-parameter when facing a new UDA task? Note that different settings are used in the office 31 and office-home dataset.

Overall, this is an interesting paper with strong theoretical analyses but weak empirical results. 

After rebuttal.

Thanks for the authors' response. After reading it, I would like to keep my score.


limitations_and_societal_impact: An explicit limitation section is needed.
review_title: null

Meta-review: This paper originally had originally some borderline negative reviews where the reviewers acknowledged a novel DA approach and  theoretical results but  noted some lack of positioning with respect to other DA methods such as DANN and some missing comparisons and justifications for the method. The authors did a very good job at answering those concerns in short and efficient replies that clarified all the major concerns from the reviewers. 

The final consensus is that the paper should be accepted. Note that the authors have to take into account the comments from the reviewed and integrate their very pertinent answers to those comments in the final version of the paper.
Decision: Accept (Poster)