Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The main contribution of the paper is to introduce and study generalized Fenchel-Young losses, which are losses for regularized energy networks that mirror Fenchel-Young losses, but where the Euclidean inner product is replaced by the energy function \Phi. They compare their losses with existing losses in the settings of multilevel classification and imitation learning.
strengths_and_weaknesses: Originality: The work can be considered a novel combination of existing techiques (Fenchel-Young losses and \Phi-conjugates). It is not strikingly original but still valuable. It is clear how the work differs from previous works, which are appropriately cited for the most part.

Quality: The work seems technically sound (I haven’t checked most proofs in the appendix).

Clarity: Some parts need to be clearer. See questions and suggestions.

Significance: The results provided are relevant as energy networks trained with generalized FY losses have better test accuracy in 4 of the 6 multilevel classification settings, and on 3 out of 4 tasks in imitation learning.
questions: - There are certain points which could be made clearer and should be expanded: (a) the paragraph in lines 140-148 (“Existing loss functions for energy networks”) is too condensed and hard to parse, it should be expanded, (b) section 6 is also hard to follow, it would be useful to explain at the beginning of the section what calibration is in this setting. On the other hand, sections 4 and 5 are reasonably clear.

- In section 6, Proposition 3, the list of properties is a bit long. Some of the properties are commented on below the proposition, but the attention of the reader gets lost, as it is not apparent which properties are most relevant. One suggestion is to defer to the appendix the properties that do not add much to the explanation.

- Computationally, how do generalized FY losses compare to the existing alternatives? It would be good to compare time.

limitations: Everything ok.
review_title: null

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: The paper introduces a class of losses based on a generalized Fenchel-Young inequality for learning energy models. The idea is to maximize the agreement between  the target $y$ and a feature $v = f(x)$ obtained using a model $f$ applied to an input $x$. The agreement is measured by minimizing an energy function $\phi(v,y)$ to which a regularization $\Omega(y)$ is added. Hence, for a given a feature $v$, the corresponding prediction $p(v)$ is given as the maximizer of the objective $\max_p F(v,p) := \phi(v,p)-\Omega(p)$. The model $f$ learned by minimizing the discrepancy between   $F(v ,y)$ and the optimal value $F(v,p(v))$. In other words, minimizing $L(v,y) = F(v,p(v))-F(v ,y)$.

The paper shows, amongst other properties, that such objectives $L$ can be optimized without the need to differentiate wrt the optimal $p(v)$ and can thus be implemented easily. 

Simple experiments show that the approach allows to consider more general losses that can yield improvement on classification and imitation learning tasks.

strengths_and_weaknesses: Strenghts:
The paper is clearly written and the results and derivations are sound. The experiments, although basic, show a marginal improvement, especially in the context of imitation learning. 

Weaknesses: Originality and Significance
Originality: The idea of extending Fenchel-Young loss, which uses an energy function given by a scalar product $ \phi(v,y)= <v,y>$ is rather direct and straightforward and does not represent a significant technical challenge. For instance, the proofs are often direct consequences of well-known results such as the envelop theorem in proposition 1.

Significance: Given that most of the experimental results show only a marginal improvement compared to more standard objectives, I am not fully convinced by the significance of the results. Do the authors have situations in mind where one requires such more general losses and where simpler approaches fail? 



 






questions: - The paragraph in L140-148 is a bit confusing: what do the authors mean by measuring the discrepancy between p_{\Omega} and $y$ without regularization Omega? Isn’t p_{\Omega} defined by a choice of a function Omega? 


- Envelope thm: The authors refer to some assumptions in the appendix under which the envelope theorem holds. These assumptions are distilled in the text of the proof. They should be explicitly stated somewhere (ideal in the main text).








limitations: The proposed approach has a rather limited novelty (both technical and conceptual). However, this can be mitigated if the authors provide more evidence for the significance of such generalization in practice.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: The most common approaches to training EBMs are approximate approaches, where the approximation comes from using MCMC to sample from the EBM. This is because training an EBM using the exact gradients is intractable, due to differentiation through argmax/argmin. This paper constructs new loss functions that can be used to tractably train an EBM using exact gradients.

The authors apply their approach to imitation learning and multilabel classification.

Note: I am not very familiar with theory, so I did not read the math sections closely.

strengths_and_weaknesses: The experiments are done with great thoroughness. The details for reproducibility are included, and the experiments are done in a robust manner (e.g. averaging over multiple seeds and properly tuning hyperparameters on validation sets).

The authors show that they are able to achieve competitive performance on multilabel classification, despite using energy networks that aren’t arbitrarily nonlinear. In other words, they show that the losses arising from the energy networks they use in these experiments are expressive enough to be accurate.

questions: None at this time
limitations: I do not see any potential negative societal impact of this work.
review_title: null

Meta-review: metareview: This paper introduces a new notion of regularized energy function using generalized Fenchel conjugates.  Reviewers were leaning towards accept, the least convinced reviewer discussed at length with the authors the contribution of the paper and the comparison of the proposed method to prior work, and leaned also towards accept after rebuttal and paper revision. Accept.
confidence: Certain
Decision: Accept