Venue: CoRL 2021 Conference

Reviews:

final_score: rating: Strong Accept: I recommend accepting the paper and will argue for my recommendation even if other reviewers hold a different opinion.
review_content: summary: The paper proposes an algorithm for performing maximum-likelihood optimization of an energy-based model over states and observations that relies on Laplace + Gauss-Newton approximation to generate contrastive samples. The algorithm is evaluated by its tracking performance and sample efficiency on synthetic navigation and real-world planar pushing tasks.
strengths_and_weaknesses: Strengths: The paper is well-written, clear, easy to follow. The approach is straightforward, interesting, and described in sufficient detail. The experiments are informative and highlight the properties of the algorithm. The video is well-done and provides a good overview of the approach.

Weaknesses: Section 3. Problem Formulation could almost entirely be removed. One could directly start with Eq. (6) that gives the standard ML objective for energy-based learning.

The Gauss-Newton method for inference is a well-known technique for sampling from intractable models. In the related work section and in Sec. 4.3 this should be clarified, because otherwise one gets an impression that the authors are claiming that they invented it. A recent overview of Laplace approximation with Gauss-Newton method, including links to prior work, can be found in [1].

The title seems misleading. In general, references to "graph" in the paper tend to obfuscate matters. In the end, what is meant is a "graphical model" or a "factor graph". But this is more-or-less standard in any paper on probabilistic modeling. One could therefore misinterpret "graph" in the title as though it were referring to graph neural networks or some algorithms for optimization over graphs. Perhaps the easiest fix would be to say "factor graph" in the title.

[1] Immer, A., Korzepa, M., & Bauer, M. (2021, March). Improving predictions of Bayesian neural nets via local linearization. In International Conference on Artificial Intelligence and Statistics (pp. 703-711). PMLR.
summary_of_recommendation: The paper considers an interesting idea of framing the observation model as an energy-based model. An approach for training this model is proposed and evaluated. The results appear encouraging and there are clear directions for future work provided. This paper may inspire further investigation into energy-based models for filtering and other applications in estimation and control.
issues: See weaknesses above
review_title: null

final_score: rating: Weak Accept: I recommend accepting the paper, but will not argue for my recommendation if the majority of other reviewers have a different opinion.
review_content: summary: The paper presents a method for learning observation models, i.e. probabilistic representations of the relationship between a latent state and sensor data, based on combining energy models with incremental Gauss-Newton solvers. The performance is evaluated on synthetic navigation and real-world object-pushing data sets.
strengths_and_weaknesses: Strengths
- The paper is well written and a pleasure to read.
- The method seems sound, and computationally efficient enough to be useful.
- The experimental results are encouraging.

Weaknesses:
I think it's a nice paper, but I have three significant concerns:
1) As a reason for ruling out "Loss 1", the authors claim that the mapping from \theta to \hat x in (3) is not differentiable. I don't understand this statement. Equation (3) states that \hat x is the minimizer of a smooth nonlinear least-squares problem. As such, it satisfies the first-order necessary conditions, and from this equation a simple application of the implicit function theorem gives the Jacobian of \hat x with respect to \theta. I think Loss 3 can still be justified on other grounds, but still this is strange.

2) Section 4.1 and 4.2 introduce the main ideas leading to Equation (7) and the associated Algorithm 1, and they read as though this is a novelty of the paper. I'm not an expert in this field, but I thought this was all completely standard in maximum-likelihood modelling. E.g. essentially the same approach is described in detail in Ch 18 of the Goodfellow et al Deep Learning book, under names such as Contrastive Divergence, e.g. Algorithm 18.1 in that book.

As far as I can see, the main novelty is using the estimated mean and covariance from the smoothing algorithm to generate the samples. The standard approach would be to use some sort of Monte-Carlo method (e.g. Gibbs sampling) to generate samples. 

I think there is a nice contribution here, but this material could more clearly describe what is actually new in the approach and what is standard.

3) Related to the above, I like the experimental results, but the choice of comparisons is a bit strange. To me, a more natural comparison would be a standard approach to Loss 3 based on MCMC. E.g. you could still use the proposed method as a proposal distribution, but then run a few iterations of a Gibbs sampler and see if that makes a difference.


summary_of_recommendation: Overall, I found this an enjoyable paper to read and I think there are some useful ideas here. I have a few issues with the paper, as described above, but these should be possible to address in a revised version.


issues: See above.
review_title: null

final_score: rating: Weak Reject: I recommend rejecting the paper, but will not argue for my recommendation if the majority of other reviewers have a different opinion.
review_content: summary: This paper applied energy-based method to solve a factor-graph optimization task (e.g., graphs that comprise factor nodes representing latent states which are connected to observation nodes). The proposed method has concrete robotic applications such as learning an observation model for a scenario concerning a robot hand manipulating an object with only tactile feedback.

The paper in particular focuses on two key points: (1) optimizing factor graph via implicit energy-based loss instead of explicit surrogate loss (i.e., using losses that parameterize the compatibility between latent states & observations instead of losses that characterizes the difference between ground-truth and explicit mapping from observations to latent states); and (2) treating factor graphs as random variables instead of fixed, unknown quantities, which relax the original discrete optimization task (over the discrete space of graphs) to a continuous optimization problem (over the continuous space of parameters defining the graph distribution).
strengths_and_weaknesses: STRENGTH:

The paper is well-written &  the mathematical exposition is not difficult to follow. The key points of the paper are well-communicated.

The proposed method has also be extensively evaluated on several datasets with clear visual demonstrations, which are really helpful in highlighting the usefulness of the proposed method

WEAKNESSES:

While this is a nice application paper, it does not exactly provide any new algorithmic and/or theoretical insights. 

In fact, both key points of (1) optimizing via energy-based implicit loss; and (2) optimizing distribution of graphs instead of graphs themselves to convert a discrete optimization task into a standard gradient-based optimization problem have been proposed and applied extensively in many fields of ML. 

In addition, the comparison with optimizing surrogate explicit loss appears minimal and lacks specific detail. Other than the vague description in line 139, I couldn't find where else in the main text such explicit loss was detailed. Aren't there existing works on the specific applications used in the experiment that the authors should have compared with?

Last, I'd suggest improving the differentiation between Loss 2 & Loss 3. Claiming that Loss 2 is surrogate & Loss 3 is energy-based (hence, implying it is not a surrogate) seems a bit misleading -- to me, the key difference is Loss 2 is based on an explicit mapping from observations to states while Loss 3 only characterize a fitness between a state configuration & the observations, which is implicit regarding the relationship between observations & latent states.
summary_of_recommendation: I think the paper is technically correct, well-motivated for an application but the entire work appears very incremental and is unlikely to have much impact regarding algorithmic novelties (e.g., both key points of the paper have been investigated and applied heavily in the ML but perhaps with different context)

I have elaborated my position in the "weaknesses" section above. That being said, I am not an expert in robotic so I am not entirely sure that this paper should be judged purely from a ML perspective -- if the other reviewers feel that the practical impact of this paper is sufficient in the robotic context, I would be happy to upgrade my rating.

But, regardless of the final outcome, I would still urge the authors to further elaborate & expand their comparison benchmark (especially against discrete graph optimizer approaches & existing works that employ explicit losses).


issues: Please refer to my specific comments in the Weakness section above.
review_title: null

Meta-review: This paper proposed an algorithm for performing maximum-likelihood optimization of an energy-based model. The approach appears to be standard by applying Laplace and Gauss-Newton approximations. The authors should justify what is new. Additionally, the authors are expected to elaborate further and expand their comparison benchmark.
Decision: Accept (Poster)