After reading the authors' rebuttal, the reviewers discussed their concerns about this paper. Ultimately, a consensus was not reached asreviewer #1 feels that the issues raised in her/his review were not properly addressed in the authors' feedback. The other reviewers also share some of the concerns raised by reviewer #1, but, given the rebuttals, they believe the authors can fix them in the final version and make the contribution of their paper clearer. I agree with them and so I suggest to accept the paper, but I recommend that the authors take into consideration the issues raised in the reviews and address them carefully in the final version of the paper.

Restricted Boltzmann Machines (RBMs) are a common family of undirected graphical models with latent variables. An RBM is described by a bipartite graph, with all observed variables in one layer and all latent variables in the other. We consider the task of learning an RBM given samples generated according to it. The best algorithms for this task currently have time complexity \tilde{O}(n 2) for ferromagnetic RBMs (i.e., with attractive potentials) but \tilde{O}(n d) for general RBMs, where n is the number of observed variables and d is the maximum degree of a latent variable. Let the \textit{MRF neighborhood} of an observed variable be its neighborhood in the Markov Random Field of the marginal distribution of the observed variables.

Originality: First-order Gradient-based MCMC methods have to deal with determining an appropriate length scale for each variable. NUTS is one approach and this paper gives another approach whereby a parameter theta of a proposal distribution is adaptively improved to account for the covariance structure. At the same time theta is adapted to consider the entropy of the proposal distribution. This trade off for theta is rolled into a new speed measure which is the central point of this paper. The paper includes a lower bound of the speed measure that can be directly differentiated resulting in a practical algorithm. The paper also includes a heuristic that makes this adaptive MCMC algorithm applicable to MALA as well.

Proposes methods to update proposal distributions for MCMC using variational-type bounds and showed it is competitive with state of the art MCMC methods. Reviewers agreed this was an important contribution.

I still feel that the work would be greatly improved by adding numerical experiments. In particular, the authors refer to a specific setting called'online MDP', where the dynamics, that is, the transition probabilities, are known while the reward is not. Regret minimization then refers to the idea to minimize the regret'' given that rewards could be chosen/observed in an adversarial manner. The authors start with a (rather technical) introduction, pose related work, and explain the main ideas based on concise preliminaries. Afterwards, an extension to large state spaces by using approximate occupancy measures and thereby avoiding concrete state-mappings is provided.

The paper contributes new algorithmic ideas and theoretical results for regret minimization in Markov Decision Processes with known transition kernels but arbitrary cost functions. The reviewers broadly agree that the theoretical and algorithmic techniques introduced by the paper -- using the FTRL online learning idea and the extension to large MDPs via linear function approximation -- are novel, and thus the paper deserves to be published; however, the known-MDP-unknown-cost setting may be somewhat narrow in its applicability in practice.

The industrial application of Deep Reinforcement Learning (DRL) is frequently slowed down because of the inability to generate the experience required to train the models. Collecting data often involves considerable time and economic effort that is unaffordable in most cases. Fortunately, devices like robots can be trained with synthetic experience thanks to virtual environments. With this approach, the sample efficiency problems of artificial agents are mitigated, but another issue arises: the need for efficiently transferring the synthetic experience into the real world (sim-to-real). This paper analyzes the robustness of a state-of-the-art sim-to-real technique known as progressive neural networks (PNNs) and studies how adding diversity to the synthetic experience can complement it. To better understand the drivers that lead to a lack of robustness, the robotic agent is still tested in a virtual environment to ensure total control on the divergence between the simulated and real models. The results show that a PNN-like agent exhibits a substantial decrease in its robustness at the beginning of the real training phase. Randomizing certain variables during simulation-based training significantly mitigates this issue. On average, the increase in the model's accuracy is around 25% when diversity is introduced in the training process. This improvement can be translated into a decrease in the required real experience for the same final robustness performance. Notwithstanding, adding real experience to agents should still be beneficial regardless of the quality of the virtual experience fed into the agent.

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.