Reviewers had agreement that this is a good contribution to stochastic optimization research. The concerns with respect to the similarity with a recent ICML paper has been addressed in the author rebuttal.

Summary The paper proposes a differentiable pipeline that can jointly learn a latent space representation (via variational autoencoder) for controlling soft robots and optimize for the controller and the soft robot parameters for tasks in simulation, such as making a soft 2D robot walk forward as fast as possible. The work is made possible by using a differentiable hybrid-particle-grid based soft material physics simulator. The authors provided insightful details on the alternative minimization scheme for training the autoencoder, the controller neural network, and the robot parameters in tandem. The proposed framework was evaluated on 5 simulated experiments that show controllers using the learned representation outperforms ones using the baseline representation obtained via k-means clustering. Review While the performance of the system is impressive, the motivation of the approach is not well-communicated in 3 folds: In discussing the proposed hybrid-particle-grid based soft robot representation vs finite element methods, the authors claim that the high "degrees of freedom of finite element methods is impractical for most modern control algorithms."

This paper formulated and proposed a solution to the problem of model selection in contextual bandits. All of the reviewers pointed out the importance of this problem and the novelty of the authors' solution. Overall, the reviews were positive about the paper and their concerns were addressed in the authors' response. The authors should make sure to update their submission to include the reviewers' suggestions, especially the empirical evaluation done in the author response.

This work introduces a geometric analysis of the problem of inverse reinforcement learning (IRL) and proposes a formal guarantee for the optimality of the reward function, obtained from the empirical data. The authors also provide the sample complexity for their proposed l1-regularized Support Vector Machine formulation. In general, this is an interesting work with a significant contribution to the theoretical aspect of the inverse reinforcement learning problem. However, there are a few concerns that need to be addressed: Major: 1. The paper does not define the problem as a stand-alone question in the field. The problem formulation heavily relies on the previous work by Ng & Russel (2000) and is written only as a follow up to this work.

More specifically, suppose we deal with n linear regression data sets after which we are challenged with a final learning task of linear regression, but the parameters of these "tasks" are not completely unrelated. In particular, suppose there is a prior distribution (with at most k possible outcomes) from which parameters of linear regression (i.e., the linear function and noise's variance) are sampled. The general idea here is that by learning from "different" (yet related) tasks the learner aims to do better on the final task, and the paper's focus is on a theoretically natural setting.

The reviewers uniformly felt that this is an interesting paper and a good contribution to the community.

Additional Feedback: Post rebuttal: Thank you for you response. I keep my score as it is (which is accept) -- but like R2, I really would like to see the finite-N results in the extra page that would be provided if this paper is accepted. The analysis looks sound and nicely done. Some elaboration on what satisfies this inequality is provided before Sec. Therefore, these results are still not precisely about the SVGD, but on its infinite-particle limit.

The reviewers agree that this paper would make a valuable contribution to NeurIPS. Please have a look at the reviewer comments (especially about moving finite-particle results to the main paper) while working on the final manuscript.

Although some techniques are analogous to previous work (which is not bad per se, as it allows to apply more general regularisers within previous frameworks such as soft-actor-critic with small changes only), this work differs significantly from previous work and yields new insights how to obtain sparse policies or not. Claims are supported by proofs and experiments confirm that considering more flexible regularizations can be beneficial in different tasks. There are some issues with the continuous time case, see the section on improvements for details. Further the authors claim that trigonometric and exponential functions families yield multimodal policies (line 287). However, it is not clear to me how this is different to say entropy regularisation, and why a softmax policy cannot have multiple modes (unless of course I parameterize the policy with a single Gaussian in the continuous case, but this is a different issue).

Weaknesses: - Below eq (3), for the upper bound of \delta_t the right-hand side should be 2\sum_s\eta_sa_s instead of 2\sum_s\eta_sa_s\delta_s . It would be interesting to add some discussions or comparison with these references mentioned below: 1. "Fine-Grained Analysis of Stability and Generalization for Stochastic Gradient Descent". In this paper, their work relaxes the smoothness to \alpha -Holder continuity of (sub)gradients, which include the non-smooth loss functions in this paper as \alpha 0 . Their stability analysis also improves the optimal generalization bounds O(1/\sqrt{n}) for multi-pass SGD with T O(n 2) . It seems to me that the main technical novelty appeared in the proof of Lemma 3 which studied \delta_t 2 (as opposed to the study of \delta_t in Hardt et al's paper) using the approximate contraction for the gradient mapping for the non-smooth loss which has already explored in the above paper. Similar ideas have already explored in the above reference in a more general setting.