{"id":"c2a22ada-1811-481e-8136-c60dede24557","arxiv_id":"2605.00237","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Recursive binary partitioning enables Bayesian optimization with linear time complexity and superior performance on test functions up to 124 dimensions.","lead":"The paper presents a Bayesian optimization approach that uses recursive binary partitioning of the search space to adapt both the Gaussian process modeling and the acquisition function, resulting in linear computational complexity. This addresses the cubic scaling and global modeling limitations of standard Bayesian optimization for expensive black-box functions.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's weakest assumption directly captures the key condition for the central claim. Because the abstract already supplies comparative results on a range of dimensions and explicitly states linear complexity, the empirical evidence addresses the practical concern. No additional load-bearing gap (such as an unstated assumption in an equation or an untested regime) is detectable without further technical details that would contradict the reported outcomes.","tokens_in":1765,"tokens_out":293,"duration_ms":44630,"concrete_test":"Re-run the seven test functions using the exact protocol from the paper (same initial points, evaluation budget, and random seeds) while logging the number of partitions created and the per-iteration wall-clock time; if observed complexity exceeds linear in n or if performance gains disappear under a different random seed set, the adaptation claim would require revision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract describes a recursive binary partitioning scheme that adapts both GP modeling and acquisition to achieve linear complexity while addressing the mismatch between global modeling and local minimization. The provided text states empirical superiority on seven test functions (6–124 dimensions) against a standard library, with no internal contradictions or unsupported leaps visible from the claim structure. The weakest assumption identified by the reader (harmonious adaptation without new biases) is plausible given the reported results, and no concrete inconsistency with the stated goals or experimental scope is evident.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript proposes a Bayesian optimization algorithm that uses flexible recursive binary partitioning of the search space to adapt both Gaussian process modeling and acquisition functions. This is claimed to resolve the cubic complexity of standard BO and the mismatch between global modeling and local minimization, yielding linear computational complexity and superior empirical performance against a standard library on seven test functions with input dimensions ranging from 6 to 124.","tokens_in":1857,"tokens_out":499,"duration_ms":24508,"significance":"If the integration of partitioning with GPs and acquisition functions is shown to preserve uncertainty quantification without introducing bias, the work would be significant for scaling Bayesian optimization to larger problems and higher dimensions where standard methods become infeasible. The reported empirical results across a range of dimensions provide a starting point for assessing practical utility, though the absence of explicit complexity derivations or theoretical guarantees in the provided text limits assessment of the core contribution.","major_comments":[{"comment":"The abstract asserts linear computational complexity and harmonious adaptation of modeling and acquisition to the partitioning scheme, but no derivation, complexity analysis, or pseudocode detailing the integration with Gaussian processes is supplied. A dedicated methods section with explicit complexity bounds (e.g., showing O(n) scaling in training-set size) is required to substantiate the central claim.","section":"Abstract / Methods"},{"comment":"The empirical comparison reports superior performance on all seven test functions, but without details on the specific acquisition function adaptation, partitioning recursion depth, or how local vs. global search is balanced within partitions, it is impossible to verify that the method avoids new biases while retaining the benefits of uncertainty-aware optimization. Include the exact experimental protocol, hyperparameter settings, and any ablation studies in §4 or §5.","section":"Experiments"}],"minor_comments":[{"comment":"The abstract mentions 'a commonly used Bayesian optimization library' without naming it or providing version/citation; add the specific reference (e.g., GPyOpt or BoTorch) for reproducibility.","section":"Abstract"},{"comment":"Test function dimensions are given as a range (6 to 124) but individual dimensions and function names are not listed; include a table in the experiments section enumerating each function, its dimension, and the number of evaluations used.","section":"Experiments"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive feedback on our manuscript. We address each major comment below and will revise the paper accordingly to improve clarity and completeness.","responses":[{"response":"We agree that the current version does not provide a self-contained derivation or pseudocode. In the revised manuscript we will insert a new dedicated Methods section that formally describes the recursive binary partitioning procedure, its integration with the Gaussian process posterior and the adapted acquisition function, the full algorithm in pseudocode, and a complexity analysis establishing O(n) scaling in the number of observations (training-set size). This will directly substantiate the linear-complexity claim.","revision_made":"yes","referee_comment":"[Abstract / Methods] The abstract asserts linear computational complexity and harmonious adaptation of modeling and acquisition to the partitioning scheme, but no derivation, complexity analysis, or pseudocode detailing the integration with Gaussian processes is supplied. A dedicated methods section with explicit complexity bounds (e.g., showing O(n) scaling in training-set size) is required to substantiate the central claim."},{"response":"We acknowledge that the experimental section currently lacks sufficient implementation detail for full reproducibility and bias assessment. We will expand Sections 4 and 5 to report the precise experimental protocol, all hyperparameter values, the exact form of acquisition-function adaptation inside each partition, the recursion-depth schedule, the mechanism used to balance local versus global search, and ablation studies that isolate the contribution of the partitioning scheme. These additions will allow readers to verify that uncertainty quantification is preserved.","revision_made":"yes","referee_comment":"[Experiments] The empirical comparison reports superior performance on all seven test functions, but without details on the specific acquisition function adaptation, partitioning recursion depth, or how local vs. global search is balanced within partitions, it is impossible to verify that the method avoids new biases while retaining the benefits of uncertainty-aware optimization. Include the exact experimental protocol, hyperparameter settings, and any ablation studies in §4 or §5."}],"tokens_in":1324,"tokens_out":430,"duration_ms":52311,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The central claim is that recursive binary partitioning lets them drop the usual cubic cost while also fixing the global-model versus local-minimization mismatch. They do this by changing how the surrogate is built and how the acquisition is computed so both respect the partitions. That integrated change is the concrete new piece, and the empirical side shows better final values than a common BO library across seven functions from 6 to 124 dimensions plus the linear scaling they advertise. Those results are the strongest part of what is here; high-dimensional scaling is a real pain point and any method that stays competitive while dropping to linear time is worth looking at. The soft spots are mostly around verification. The abstract gives no derivation or complexity breakdown, so it is not yet clear whether the partitioning preserves the uncertainty estimates that make BO useful or whether the adapted acquisition still balances exploration properly. The test functions are standard synthetic ones, which is fine for a first check but leaves open how the method behaves on the noisy, constrained, or multi-fidelity problems that actually drive most BO use. If the full paper supplies the missing equations, a reproducible implementation, and at least a sketch of why the complexity stays linear end-to-end, those gaps close quickly. This is for readers who already work on scalable surrogates or tree-structured optimization and want to see one concrete way the pieces can be made to fit. It is worth sending to a serious referee because the problem is well-motivated, the proposed fix is specific, and the reported gains are large enough to justify checking the details rather than desk-rejecting.","headline":"The paper adapts Bayesian optimization to linear time by recursively partitioning the space and syncing both the GP surrogate and acquisition function to it, with reported wins over a standard library on tests up to 124 dimensions.","tokens_in":2369,"tokens_out":398,"would_cite":false,"duration_ms":53779,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Recursive binary partitioning adapts Bayesian optimization to linear time and better performance on high-dimensional tests.","keywords":["Bayesian optimization","linear complexity","binary partitioning","Gaussian processes","acquisition functions","black-box optimization","high-dimensional optimization"],"falsifier":"Runtime measurements showing super-linear growth as the number of evaluations increases, or the method returning higher final values than standard Bayesian optimization on new test functions with known optima.","tokens_in":2641,"feed_emoji":"⏱️","tokens_out":525,"duration_ms":37730,"temperature":0.7,"pith_summary":"Standard Bayesian optimization trains a Gaussian process on all prior evaluations and uses an acquisition function to pick the next point by mixing exploration and exploitation. This produces cubic scaling in the number of points and applies a single global model even though the minimum is typically local. The paper shows that recursively splitting the domain into binary partitions lets both the model and the acquisition function operate inside each subregion. The resulting method runs in linear time and reaches lower objective values than a standard library on seven benchmark functions whose dimensions range from 6 to 124.","feed_headline":"Recursive partitioning enables linear-time Bayesian optimization","feed_subtitle":"The method outperforms a standard library on benchmarks from 6 to 124 dimensions while avoiding cubic costs.","key_machinery":"Flexible recursive binary partitioning of the search space, which localizes both the Gaussian process surrogate and the acquisition function within each subregion.","core_discovery":"Using flexible and recursive binary partitioning of the search space, both the modeling and acquisitive aspects of standard Bayesian optimization are adapted to work harmoniously with the partitioning scheme. This change removes the cubic computational bottleneck and aligns the search process more closely with the local character of minimization.","pith_inferences":["Partitioning ideas of this kind could be applied to other surrogate-based sequential methods that currently face cubic scaling limits.","Real engineering or hyperparameter tasks with costly evaluations might now support longer search runs without computational collapse.","Adaptive rules for choosing split locations could further improve performance on functions with sharp local features."],"forward_implications":["The approach scales to optimization budgets far larger than those feasible with cubic methods.","Better final objective values are obtained on high-dimensional black-box problems.","Computational cost grows linearly rather than cubically with the number of observations collected.","The local nature of minimization is respected while still using uncertainty to guide sampling."],"fun_headline_variants":["Recursive partitioning linearizes Bayesian optimization","Linear-time Bayesian optimization via recursive partitioning","Binary partitioning linearizes Bayesian optimization","Space partitioning for linear-time Bayesian optimization"],"cache_read_input_tokens":64,"weakest_assumption_plain":"That recursive binary partitioning integrates with Gaussian process modeling and acquisition functions without introducing biases that degrade the quality of the uncertainty-aware search.","fun_headline_variants_meta":{"raw":{"variants":["Recursive partitioning linearizes Bayesian optimization","Linear-time Bayesian optimization via recursive partitioning","Binary partitioning linearizes Bayesian optimization","Space partitioning for linear-time Bayesian optimization"]},"model":"grok-4.3","cost_usd":0.0085,"raw_usage":{"total_tokens":3729,"prompt_tokens":604,"num_sources_used":0,"completion_tokens":47,"cost_in_usd_ticks":85003000,"prompt_tokens_details":{"text_tokens":604,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3078,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":604,"tokens_out":47,"duration_ms":39078,"temperature":1.0,"reasoning_tokens":3078,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-09T20:16:11.883540+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Runtime measurements showing super-linear growth as the number of evaluations increases, or the method returning higher final values than standard Bayesian optimization on new test functions with known optima.","supporting_citations":[],"review_version":1}