Additional Feedback: Post-rebuttal The authors addressed some of my concerns. As the authors would redesign some of the experiments in the revision, I'd raise my score to 6. Comments and questions: 1. Are there any lower bound results on the sample complexity of planning? Are there any particular reasons, and what is the high-level idea of this algorithm? If I understand correctly this rule is to get the gap-dependent sample complexity. What if we use the simple greedy policy for the first action, and what will go wrong in the proof?

The reviewers unanimously agree that the paper makes a nice contribution to the MCTS literature and offers novel algorithmic and analytical ideas.

This work provides a detailed Renyi DP analysis of a modified MCMC acceptance test, and empirically demonstrates its efficacy. Originality: the RDP analysis and modified acceptance test is a novel contribution. Quality: the work is a complete piece on exploring this MCMC method, with a detailed analysis and experiments. Clarity: the work is fairly clearly written, but it can be easy to lose track of exactly what parameters remain as choices to be tuned in a list of various corrective factors and approximations. Significance: the work gives an MCMC method with privacy without convergence, which permits privacy guarantees to be given over a multitude of problems without doubts or guess work about when to stop the chain.

Although the analysis follows some known ideas from the literature on private SGD, there are a number of new tricks which make the current approach interesting, most notably the observation that one can use randomized acceptance tests to preserve privacy in an MCMC algorithm. When preparing the final version of this manuscript the authors should carefully consider the points raised in the reviews regarding: clarifying where the contributions lie with respect to previous work; provide high-level intuitions of the proofs to help a reader navigate the derivations; discuss the role of approximations used in the paper, where they affect the privacy or utility of the method, and where there is some room left for improvement.

This paper studies the problem of learning soft state aggregation of a Markov model, where there are r hidden meta states, each corresponds to a distribution over the observed state of the Markov model. Under the anchor state assumption, the authors propose an algorithm that provably learns the state aggregation model from the Markov chain's trajectory. They evaluated their algorithm on a Manhattan taxi-trip dataset which yields interesting discoveries. There has been lots of work on estimating the low rank transition matrix itself and on matrix factorization in the topic modelling setting, and this work seems to be connecting the two problems. The paper is presented well and easy to follow. I have the following questions regarding the novelty and impact of this paper.

The study of learning causal structure with latent variables has advanced the understanding of the world by uncovering causal relationships and latent factors, e.g., Causal Representation Learning (CRL). However, in real-world scenarios, such as those in climate systems, causal relationships are often nonparametric, dynamic, and exist among both observed variables and latent variables. These challenges motivate us to consider a general setting in which causal relations are nonparametric and unrestricted in their occurrence, which is unconventional to current methods. To solve this problem, with the aid of 3-measurement in temporal structure, we theoretically show that both latent variables and processes can be identified up to minor indeterminacy under mild assumptions. Moreover, we tackle the general nonlinear Causal Discovery (CD) from observations, e.g., temperature, as a specific task of learning independent representation, through the principle of functional equivalence. Based on these insights, we develop an estimation approach simultaneously recovering both the observed causal structure and latent causal process in a nontrivial manner. Simulation studies validate the theoretical foundations and demonstrate the effectiveness of the proposed methodology. In the experiments involving climate data, this approach offers a powerful and in-depth understanding of the climate system.

Traditional approaches to studying decision-making in neuroscience focus on simplified behavioral tasks where animals perform repetitive, stereotyped actions to receive explicit rewards. While informative, these methods constrain our understanding of decision-making to short timescale behaviors driven by explicit goals. In natural environments, animals exhibit more complex, long-term behaviors driven by intrinsic motivations that are often unobservable. Recent works in time-varying inverse reinforcement learning (IRL) aim to capture shifting motivations in long-term, freely moving behaviors. However, a crucial challenge remains: animals make decisions based on their history, not just their current state. To address this, we introduce SWIRL (SWitching IRL), a novel framework that extends traditional IRL by incorporating time-varying, history-dependent reward functions. SWIRL models long behavioral sequences as transitions between short-term decision-making processes, each governed by a unique reward function. SWIRL incorporates biologically plausible history dependency to capture how past decisions and environmental contexts shape behavior, offering a more accurate description of animal decision-making. We apply SWIRL to simulated and real-world animal behavior datasets and show that it outperforms models lacking history dependency, both quantitatively and qualitatively. This work presents the first IRL model to incorporate history-dependent policies and rewards to advance our understanding of complex, naturalistic decision-making in animals. Historically, decision making in neuroscience has been studied using simplified assays where animals perform repetitive, stereotyped actions (such as licks, nose pokes, or lever presses) in response to sensory stimuli to obtain an explicit reward. While this approach has its advantages, it has limited our understanding of decision making to scenarios where animals are instructed to achieve an explicit goal over brief timescales, usually no more than tens of seconds.

Hippocampal formation (HF) can rapidly adapt to varied environments and build flexible working memory (WM). To mirror the HF's mechanism on generalization and WM, we propose a model named Generalization and Associative Temporary Encoding (GATE), which deploys a 3-D multi-lamellar dorsoventral (DV) architecture, and learns to build up internally representation from externally driven information layer-wisely. In each lamella, regions of HF: EC3-CA1-EC5-EC3 forms a re-entrant loop that discriminately maintains information by EC3 persistent activity, and selectively readouts the retained information by CA1 neurons. CA3 and EC5 further provides gating function that controls these processes. After learning complex WM tasks, GATE forms neuron representations that align with experimental records, including splitter, lap, evidence, trace, delay-active cells, as well as conventional place cells. Crucially, DV architecture in GATE also captures information, range from detailed to abstract, which enables a rapid generalization ability when cue, environment or task changes, with learned representations inherited. GATE promises a viable framework for understanding the HF's flexible memory mechanisms and for progressively developing brain-inspired intelligent systems.

I found the paper very well presented and enjoyable to read. The basic problem is interesting, and the approach presented as some salient features, notably the fact that one does not have to make parametric assumption on the underlying distribution. The high-level idea of imposing structural assumptions but nonetheless relying on discriminative models was quite elegant. The basic insight in estimating the risk from unlabelled data is that by encoding a certain structural assumption - namely, that the data comprises three independent views - one implicitly gets information about the class-conditional risks by considering the first three moments of the label vectors. This leads to a system of equations which may be solved to infer the class-conditional risks.

Optimization of the link structure for PR is not a new topic. Apart from papers mentioned in Related work, there are also those not reviewed, including "PageRank Optimization by Edge Selection" by Csaji et al., "Maximizing PageRank with New Backlinks" by Olsen, "PageRank Optimization in Polynomial Time by Stochastic Shortest Path Reformulation" by Csaji et al. **The novelty** of the study is questionable. The probability of reaching the target state \sigma can be viewed as the state's stationary probability for the graph, where the added edges are directed to the state \sigma and the matrix of transition probabilities is raised to an appropriate power. This observation does not immediately reduce the problem of the paper to a known task, however, it may partially explain the similarity between the theoretical part and the works of Olsen, where the stationary probability is maximized. In particular, Section 4 resembles the work "Maximizing PageRank with New Backlinks" (not cited in the paper), where M. Olsen considered a reduction of a Markov chain optimization problem to the independent set problem, which is equivalent to the vertex cover problem. Theorems 5.1, 5.3 are reasonable, but very simple and resemble Lemmas 1,2 from [15].