Existing score-based methods for directed acyclic graph (DAG) learning from observational data struggle to recover the causal graph accurately and sample-efficiently. To overcome this, in this study, we propose DrBO (DAG recovery via Bayesian Optimization)-a novel DAG learning framework leveraging Bayesian optimization (BO) to find high-scoring DAGs. We show that, by sophisticatedly choosing the promising DAGs to explore, we can find higher-scoring ones much more efficiently. To address the scalability issues of conventional BO in DAG learning, we replace Gaussian Processes commonly employed in BO with dropout neural networks, trained in a continual manner, which allows for (i) flexibly modeling the DAG scores without overfitting, (ii) incorporation of uncertainty into the estimated scores, and (iii) scaling with the number of evaluations. As a result, DrBO is computationally efficient and can find the accurate DAG in fewer trials and less time than existing state-of-the-art methods. This is demonstrated through an extensive set of empirical evaluations on many challenging settings with both synthetic and real data. Our implementation is available at https://github.com/baosws/DrBO.

This paper proposes a novel approach to formulate time-optimal point-to-point motion planning and control under uncertainty. The approach defines a robustified two-stage Optimal Control Problem (OCP), in which stage 1, with a fixed time grid, is seamlessly stitched with stage 2, which features a variable time grid. Stage 1 optimizes not only the nominal trajectory, but also feedback gains and corresponding state covariances, which robustify constraints in both stages. The outcome is a minimized uncertainty in stage 1 and a minimized total motion time for stage 2, both contributing to the time optimality and safety of the total motion. A timely replanning strategy is employed to handle changes in constraints and maintain feasibility, while a tailored iterative algorithm is proposed for efficient, real-time OCP execution.

Weaknesses: My main concerns are whether this work makes an impactful contribution to the type of problems of interest to the NeurIPS community. The problem of high-dimensional integration is of course of vital importance in many areas of machine learning, appearing centrally for example in Bayesian inference/model selection, graphical models, and the training of latent variable generative models, and many of us would welcome an addition to the toolkit of dealing with such beasts. Unfortunately, this paper makes only minimal effort to motivate the relevance of the proposed QMC construction to these settings. An application to GAN/VAEs does briefly appear in the supplementary, but with quite cursory quantification of performance; showing sharper generated images is not consistent with the rigorous aims and tone of the paper. For a NeurIPS audience, I consider it essential to include a comparison against established sampling algorithms such as Sequential Monte Carlo.

This assumption is crucial for dynamic programming type of analysis. Although it seems to be just an assumption on the value function class, it actually also implicit makes assumption about the MDP. The difference between the sensitive sampling in this paper and the prior work also need to be discussed more. Moreover, the connection between Lemma 9 and 10 and Proposition 3 and Lemma 2 in [44] also need to be discussed. I think these discussions will be helpful for people to understand the details and digest the proof.

The problem of exploration in RL with function approximation is very important and any advancement on the topic is of interest for the community. The reviewers all agreed about the algorithmic and technical contribution of the paper, in particular the introduction of sensitive sampling and its analysis in the regret proof. This convinced us that the paper deserves acceptance. Nonetheless, I also encourage the authors to improve the current submission. As pointed out by R3, the assumptions used in the paper are quite strong and they may somehow limit the generality of the results.

This is an interesting paper, and well written. Overall I like the contributions. I have the following comments to consider. I am not sure "feedforward" is an appropriate prefix for the technique, as it seems to suggest that the approach is feedforward neural networks based. Though, it is completely upto the authors.

This paper proposes two algorithms for recovering ground truth labels in crowd sourcing tasks for binary classisification. The problem is formulated as an online Bayesian version of the Dawid & Skene model (with beta priors) which is quite natural. The algorithms are based on variational approximations of the posterior (i.e. they try to find the best approximation that is product distribution). From this approach two algorithms are derived. The other one is more accurate and but slower (still polynomial time).

Given the space constraint of the rebuttal, I will trust the authors to indeed incorporate the changes as promised, and given this I increased my score. However, at several places in this paper, it is too dense to follow. More detailed comments are as follows. First, this paper lacks a dedicated related work section. There is some brief discussion about how this work differs from existing literature, in the introduction, yet it is not enough.

This paper proposes a Bayesian formulation for SPN models. All reviewers felt this formulation had merit, and there was agreement with the authors on possible improvments.

Weaknesses: The paper emphasizes its focus on causal structure learning. In doing so it assumes "causal sufficiency", that is, it assumes that there are no latent confounders of the measured variables. Generally, there are many latent confounders of the measured variables in most domains. In the past 20 years, there has been substantial progress in developing graphical representations and algorithms for learning equivalence classes of causal networks from observational data. When causal sufficiency is assumed, the learning of DAG structure is generally called Bayesian network structure learning, not causal structural learning, as in the title of the paper. It would be helpful for the paper to more prominently highlight this assumption.