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.

Unmanned Aerial Vehicles (UAVs) are pivotal in applications such as search and rescue and environmental monitoring, excelling in intelligent perception tasks. However, their limited battery capacity hinders long-duration and long-distance missions. Charging UAVs (CUAVs) offers a potential solution by recharging mission UAVs (MUAVs), but existing methods rely on impractical pre-planned routes, failing to enable organic cooperation and limiting mission efficiency. We introduce a novel multi-agent deep reinforcement learning model named \textbf{H}eterogeneous \textbf{G}raph \textbf{A}ttention \textbf{M}ulti-agent Deep Deterministic Policy Gradient (HGAM), designed to dynamically coordinate MUAVs and CUAVs. This approach maximizes data collection, geographical fairness, and energy efficiency by allowing UAVs to adapt their routes in real-time to current task demands and environmental conditions without pre-planning. Our model uses heterogeneous graph attention networks (GATs) to present heterogeneous agents and facilitate efficient information exchange. It operates within an actor-critic framework. Simulation results show that our model significantly improves cooperation among heterogeneous UAVs, outperforming existing methods in several metrics, including data collection rate and charging efficiency.

Precise and real-time estimation of the robotic arm's position on the patient's side is essential for the success of remote robotic surgery in Tactile Internet (TI) environments. This paper presents a prediction model based on the Transformer-based Informer framework for accurate and efficient position estimation. Additionally, it combines a Four-State Hidden Markov Model (4-State HMM) to simulate realistic packet loss scenarios. The proposed approach addresses challenges such as network delays, jitter, and packet loss to ensure reliable and precise operation in remote surgical applications. The method integrates the optimization problem into the Informer model by embedding constraints such as energy efficiency, smoothness, and robustness into its training process using a differentiable optimization layer. The Informer framework uses features such as ProbSparse attention, attention distilling, and a generative-style decoder to focus on position-critical features while maintaining a low computational complexity of O(L log L). The method is evaluated using the JIGSAWS dataset, achieving a prediction accuracy of over 90 percent under various network scenarios. A comparison with models such as TCN, RNN, and LSTM demonstrates the Informer framework's superior performance in handling position prediction and meeting real-time requirements, making it suitable for Tactile Internet-enabled robotic surgery.

I am changing the score to 7. The paper gives a new algorithm for learning the structure Restricted Boltzmann Machines (formalized using Markov blankets), which is claimed to work for larger parameter regimes than the previous work. This is done by considering the problem of predicting the spin of a node given the spins of all other nodes. This dependence is shown to be given by a one-hidden layer neural net (with somewhat non-standard activations). An algorithm for learning this network is given based on polynomial approximation of the neural net and using regression on degree-D monomial feature map (with \ell_1 constraint). The algorithm works under L_\inf constraint on the input vector which is different from the past work. Given the above algorithm for learning the dependence of one node on the rest, under suitable non-degeneracy conditions, an algorithm is given for learning the structure (Markov blanket) of the RBM. Nearly matching lower bounds are provided (under hardness assumptions or in the SQ model). The reduction to neural networks is also used for learning supervised RBMs, which can be thought of as a neural network under distributional assumptions on the data (in terms of "sparsity and nonnegative correlations among the input features 307 conditional on the output label"). This distributional assumptions seems to be new.

The initial scores in the four reviews were all in favour of accepting, although not strongly. The paper studies a relevant problem, presenting a new algorithm with performance guarantees and almost matching lower bounds. However some questions were raised regarding, for example, connections to other work and practical algorithms, and also more technical issues. The authors provided a detailed reply. After discussion among the reviewers, their concerns were partially answered, leading to somewhat stronger support for accepting.

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.

All of the reviewers agree that this paper is both theoretically and modeling-wise a solid contribution to NeurIPS. My only concerns are that some of the author rebuttal points have not made it into the paper -- all of them should be added I think, in particular the related work (extended), the causal sufficiency clarification, and the run times.

This theoretical paper considers the problem of computing optimal value function in entropy-regularized MDPs and two-player games. It shows that the smoothness property of the Bellman operator in the presence of entropy regularized policies (and possibly other forms of regularization), can be used to derive a sample complexity which is polynomial of order O((1/ε) {4 c}), with c being a problem independent constant and ε the precision of the value function estimate. The proof is built upon the proposed algorithm, SmoothCruiser, an algorithm motivated in the sparse sampling algorithm of Kearns et al that recursively estimates V through samples and subsequently aggregates the results. This sampling dynamic programming is done up to a depth when the required number of samples is no longer polynomial. The paper is very well written and provides a solid result.