Title: KeeA*: Epistemic Exploratory A* Search via Knowledge Calibration
Venue: NeurIPS 2025
Accepted: yes
Keywords: A* search

neural guided heuristic search

retrosynthesis planning
Abstract: In recent years, neural network-guided heuristic search algorithms, such as Monte-Carlo tree search and A$^\*$ search, have achieved significant advancements across diverse practical applications. Due to the challenges stemming from high state-space complexity, sparse training datasets, and incomplete environmental modeling, heuristic estimations manifest uncontrolled inherent biases towards the actual expected evaluations, thereby compromising the decision-making quality of search algorithms. Sampling exploration enhanced A$^\*$ (SeeA$^\*$) was proposed to improve the efficiency of A$^\*$ search by constructing an dynamic candidate subset through random sampling, from which the expanded node was selected. However, uniform sampling strategy utilized by SeeA$^\*$ facilitates exploration exclusively through the injection of randomness, which completely neglects the heuristic knowledge relevant to open nodes. Moreover, the theoretical support of cluster sampling remains ambiguous. Despite the existence of potential biases, heuristic estimations still encapsulate certain valuable information. In this paper, epistemic exploratory A$^\*$ search (KeeA$^\*$) is proposed to integrate heuristic knowledge for calibrating the sampling process. We first theoretically demonstrate that SeeA$^\*$ with cluster sampling outperforms uniform sampling due to the distribution-aware selection with higher variance. Building on this insight, cluster scouting and path-aware sampling are introduced in KeeA$^\*$ to further exploit heuristic knowledge to increase the sampling mean and variance, respectively, thereby generating higher-quality extreme candidates and enhancing overall decision-making performance. Finally, empirical results on retrosynthetic planning and logic synthesis demonstrate superior performance of KeeA$^*$ compared to state-of-the-art heuristic search algorithms.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a new search algorithm that incorporates several modifications compared to the SeeA* algorithm. First, the paper provides theoretical evidence that sampling within clusters can increase the likelihood of finding good solutions since this increases the variance of the reward among the candidate nodes to be expanded. Compared to SeeA*, the paper introduces cluster scouting, where samples within each cluster are evaluated to determine a score for each cluster which is used to bias candidate node sampling towards the clusters with a higher score. The paper also introduces a method for intra-cluster sampling that biases candidate node selection towards nodes that have been expanded fewer times. This algorithm is then evaluated on two sets of benchmarks involving retrosynthetic planning and logic synthesis.\n\nSTRENGTHS AND WEAKNESSES:\n**Quality**: The first two claims in the paper, concerning the theoretical foundation for cluster sampling and the rationale for introducing cluster scouting and path-aware sampling, are well supported by the theoretical and empirical evidence. However, I do see two issues with the implementation of cluster scouting. First, and this is a point I may have misunderstood, is that this appears to be a computationally intensive process since it requires evaluating a potentially large number of reward functions to determine the score for each cluster. I expect this could be a limitation of this method compared to SeeA*. Second, I’m not convinced dividing the expectation value of the reward by the standard deviation is a good way of assessing the score. This would attribute a higher score to clusters with very low rewards but much smaller standard deviation than it would to clusters with much higher rewards and a higher (but still potentially quite small) standard deviation. I also have a concern about how path-aware sampling is combined with cluster scouting. Cluster scouting may return high scores to clusters where the reward for deeper nodes is much higher than shallower nodes, but the path-aware sampling would then focus on the shallower nodes which is counter-productive. I feel a more principled sampling approach would include the expansion depth into the score.\n\nThe third claim concerns the experimental benchmarking. A strength of the paper is that the experiments are extensive and contain a statistical robustness test for the results. However, a weakness is that the results for KeeA* are very close to those of SeeA*. Though the statistical tests run in the paper show that the difference is statistically significant, these tests do not rule out the possibility that these better results are achieved through overfitting the hyperparameters of KeeA* to the specific problems investigated in the experiments. This concern is reinforced by results in the appendix that show that the performance sometimes seems to vary by more than the difference between the two algorithms for different (but close) hyperparameter choices. Another concern I have about these experiments is that they do not include SeeA* with UCT as a baseline in the benchmarks. The SeeA* paper shows that SeeA* with UCT outperforms KeeA* on the USPTO dataset in both success rate and average runtime. Considering UCT plays a similar role as path-aware sampling, I feel this is a valid baseline that should have been included in this comparison.\n\nThough the paper does mention some limitations, some additional discussion of these limitations would have been welcome. For instance, more information about the variability of KeeA* due to sampling randomness would be welcome.\n\n**Clarity**: The paper is clear and well-written. Extensive additional information is provided in the appendix. There are a few minor typos that need correcting. A minor detail is that how clusters are made and maintained in the nodes is not explained in the main text apart from Algorithm 1. It would help the reader to include a small discussion of this before section 4 that discusses the motivation for these clusters.\n\n**Significance**: The paper proposes some interesting directions for improving SeeA*, and I can see some of these being picked up by the community. The observation that sampling from clusters is a theoretically well-founded way of improving performance is useful and does motivate further exploration of ways in which clusters could be better defined and sampled from. The expanded evaluation on multiple retrosynthetic planning datasets compared to SeeA* is also a step forward. However, the very small performance improvement over SeeA* limits the significance of the work.\n\n**Originality**: The way in which KeeA* investigates and makes use of different clusters, and the evaluation on additional retrosynthetic datasets, are original and interesting. This work is well-referenced and is appropriately compared to prior work. However, some of the contributions in this paper appear somewhat incremental. The observation that cluster sampling can lead to higher variance in the samples is quite intuitive, and there is little additional insight provided by the mathematical proof. Theorem 5.1 is also quite basic and does not add new insight.\n\nQUESTIONS:\n1)\tPlease provide more information about the additional overhead involved in the reward function estimations that are required to assign scores to clusters. This seems to be a potentially limiting factor.\n2)\tPlease provide a comparison of this work to SeeA* with UCT, and explain why this was not included as a baseline in the benchmarking. This seems to be a very relevant comparison that is currently missing.\n3)\tCould you please include more information about the variability of KeeA* due to randomness, for example how the performance changes between different seeds on a given problem?\n4)\tCould the authors please respond to my concerns about their choice of score metric for the clusters, and discuss the interplay with path-aware sampling? I am not currently convinced these are good design choices in KeeA*.\n5)\tCould the authors please respond to my concerns that the performance improvement compared to SeeA* could be due to overfitting KeeA*’s hyperparameters to these problems, instead of an underlying algorithmic advantage?\nA satisfactory answer to these questions could improve my “Quality” score.\n\nLIMITATIONS:\nLimitations are only addressed superficially in the conclusion. More information specifically about the variability due to randomness would be appreciated.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-27"}

comments: SUMMARY:
This paper proposed a heuristic search algorithm called Keep A*, which utilizes a cluster sampling instead of a simple random sampling. Experimental evaluations on extensive real-world datasets demonstrated the effectiveness of the proposed method. Furthermore, the authors provided theoretical backgrounds of Keep A* to clarify the reasons for the performance improvements by Keep A*.

STRENGTHS AND WEAKNESSES:
Strengths
1. Clear motivation and extensive related work study supporting the motivation of the proposed method.

2. Theoretical analysis that clarifies the reasons for the performance improvements by the proposed method.

3. State-of-the-art performance on real-world datasets.


Weaknesses
1. Which of the following categories does the proposed cluster sampling belong to: distance-based, density-based, or their combination? Each clustering method has inherent advantages and disadvantages. Please clarify the advantages and disadvantages of the cluster sampling. It will be helpful in justifying the proposed method.

2. I was not able to fully analyze the reasons for the accuracy improvements by Keep A* in the the retrosynthetic planning problems because the problem definition of the retrosynthetic planning is not clear. In the current problem definition, I didn't fully understand why state-of-the-art machine learning algorithms for organic retrosynthesis have not been compared in the experiments.

3. K is a crucial hyperparameter in the clustering methods with a fixed K. However, a hyperparameter analysis of K is not provided in the manuscript. If I missed the description of K, please let me know where the description of K is.

QUESTIONS:
See the Strengths And Weaknesses section.

LIMITATIONS:
See the Strengths And Weaknesses section.
TITLE: Official Review
CLARITY: 2
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-02

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes KeeA*, an extension of SeeA* that augments selective‑sampling A* search with two knowledge‑guided mechanisms, cluster scouting and path‑aware sampling. A theoretical argument shows that cluster sampling should raise the expected extreme reward relative to uniform sampling, after which the two new heuristics are introduced to further raise the candidate‑set mean and variance. Experimental results cover retrosynthetic planning and logic‑synthesis benchmarks and include ablations and a McNemar test for significance.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n\n+ The topic is timely: many modern search systems rely on neural heuristics whose bias can cripple performance, and methods that inject principled exploration are valuable. \n\n+ The theoretical development, while idealised, cleanly connects distributional variance to extreme‑value rewards and clarifies why cluster sampling helps. KeeA* moves beyond a conceptual observation by designing concrete, lightweight modifications that integrate readily with SeeA*, so the methodological increment is small in implementation but effective in practice. \n\n+ The two applications, retrosynthetic planning in organic chemistry and logic synthesis in VLSI design, are interesting and the performance shows clear evidence the proposed method outperforms existing state-of-the-art methods.\n\nWeaknesses\n- The analysis in Theorem 5.1 still rests on homoscedastic Gaussian error assumptions. In practice, heuristic inaccuracies are heavy‑tailed and state‑dependent; some discussion of robustness would help readers better understand applicability. \n\n- While the authors use consistent \\alpha and \\beta, baseline hyper‑parameter parity is not fully demonstrated: different search algorithms may require different choices of \\alpha and \\beta to achieve the optimal performance. Part of KeeA*’s gain may just come from the fact that the current setup of \\alpha and \\beta works better compared to the baselines. A small grid search on both SeeA* and KeeA* might dispel this doubt.\n\nQUESTIONS:\n+ Typos such as “an dynamic subset” (abstract) and a few inconsistent variable names between Algorithm 1 and the appendix remain. \n\n+ Figures 3-5 lack confidence intervals; error bars would complement the McNemar test. The derivation in Appendix B occasionally drops expectation brackets, which may confuse readers unfamiliar with the notation.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-02"}

comments: SUMMARY:
This paper introduces KeeA*, an epistemic exploratory A* search method that incorporates heuristic knowledge to refine the sampling process. Through theoretical analysis, they first prove that SeeA* with cluster sampling outperforms uniform sampling by leveraging distribution-aware selection. Built on this, KeeA* introduces two key techniques: 1) cluster scouting, which increases the sampling mean, and 2) path-aware sampling, which enhances the sampling variance. These advancements enable KeeA* to generate higher-quality extreme candidates. Empirical evaluations on retrosynthetic planning and logic synthesis confirm that KeeA* achieves superior performance compared to state-of-the-art heuristic search algorithms, e.g., SeeA*, A*, MCTS, etc.

STRENGTHS AND WEAKNESSES:
Strength:
1) How to effectively leverage heuristic knowledge relevant to open nodes is a important question to explore in search algorithms.
2) Theretical analysis on cluster sampling and the two proposed techniques is novel and robust.
3) Experiment design and execution are excellent, with KeeA* demonstrating clear performance improvements over the baselines.

Weaknesses:
1) Discuss on application scenarios where KeeA* might underperform compared to SeeA*.

QUESTIONS:
Discuss on application scenarios where KeeA* might underperform compared to SeeA*

LIMITATIONS:
No
TITLE: Official Review
CLARITY: 4
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-05