Efficient optimization of expensive black-box simulators via marginal means, with application to neutrino detector design

Alan Poon; Ann-Kathrin Schuetz; Hwanwoo Kim; Simon Mak

REVIEW 3 major objections 2 minor 1 cited by

Efficient optimization of expensive black-box simulators via marginal means, with application to neutrino detector design

T0 review · 3 major / 2 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper proposes a black-box optimization estimator that uses marginal mean functions to pick solutions beyond the evaluated inputs, and proves it is consistent with a rate that tempers the curse of dimensionality.

desk verdict The abstract describes a potentially useful BOMM estimator with a claimed rate theorem, but the supplied full text is the wrong paper, so none of the central claims can be checked. read the letter →

arxiv 2508.01834 v2 pith:EC2JAGUI submitted 2025-08-03 stat.ML cs.LGstat.COstat.ME

Hwanwoo Kim , Simon Mak , Ann-Kathrin Schuetz , Alan Poon This is my paper · ORCID

classification stat.MLcs.LGstat.COstat.ME

keywords black-boxoptimizationmarginalmeansgeneralizedadditivemodelcurseofdimensionalityGaussianprocesssurrogateexpensivesimulatorsneutrinodetectordesign

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper confronts a practical bottleneck: when each run of an expensive simulator costs hundreds of CPU hours, the best point from a handful of evaluated inputs, the 'pick-the-winner' solution, is usually far from optimal, and the gap grows with dimension. Its proposed BOMM estimator instead builds marginal mean functions that summarize how the objective responds to each input coordinate, and uses them to propose a global optimizer that need not be among the evaluated points. Under a generalized additive model with an unknown link function, the paper proves the estimator is consistent for optimization and that its convergence rate tempers the curse of dimensionality, meaning it can improve as dimension grows where existing methods degrade. The paper also provides a practical implementation with a transformed additive Gaussian process surrogate and demonstrates the method on neutrino detector design, where each simulator run is costly.

What carries the argument

The key object is the marginal mean function for each input coordinate: a one-dimensional curve obtained by averaging the objective over the other coordinates within the generalized additive model. The BOMM estimator is built by inferring these marginals from the evaluated runs and then finding the coordinate-wise points where they are optimized; under the additive structure, the coordinate-wise optima jointly recover the global optimizer. The practical surrogate is a transformed additive Gaussian process, which provides a way to estimate the unknown link and the marginal means from limited data without requiring the link to be specified in advance.

What would settle it

Take a black-box function with known strong interactions, for example $f(\mathbf{x}) = x_1 x_2$ plus noise, run BOMM with a fixed small budget at moderate dimension, and compare the recovered optimum to the best evaluated point and to the known true optimum. If BOMM consistently fails to approach the true optimum or is no better than pick-the-winner as the dimension grows, the generalized-additive assumption is doing the work rather than the estimator.

Watch

Extended reading notes

Core claim

The central claim is that the global optimizer of an unknown black-box objective can be recovered from marginal mean functions rather than from the best observed output. For an objective that follows a generalized additive model, the BOMM estimator is consistent: with enough runs it recovers the true optimizer, even though no run may land near it. More strongly, the estimator's optimization rate tempers the curse of dimensionality; as the abstract states, it enables better performance as dimensionality increases, in contrast to pick-the-winner style methods whose error typically worsens sharply with dimension. This is a methodological discovery about how to allocate limited simulator budget, shifting the goal from selecting among evaluated points to constructing a better point from learned structure.

Load-bearing premise

The load-bearing premise is that the true objective is well approximated by a generalized additive model with an unknown link function; if the simulator's response has substantial interactions among input coordinates, the consistency and rate guarantees need not hold.

Editorial extensions

If this is right

With a fixed simulator budget, BOMM can nominate candidate inputs that were never evaluated, potentially giving a better design than any run actually performed.
The proven consistency provides a theoretical guarantee that the proposed optimizer converges to the true one under the assumed model, filling a gap where many black-box optimization heuristics lack guarantees.
The optimization rate tempers the curse of dimensionality, so adding input dimensions need not destroy performance at the same rate as existing methods.
The transformed additive Gaussian process surrogate gives a concrete, practical route to implement the estimator rather than leaving it as a theoretical construct.
The demonstrated neutrino detector application suggests the method is directly useful for expensive physics simulators where runs take hundreds of CPU hours.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural extension the paper does not pursue is applying the same marginal-means logic to other costly evaluation problems, such as hyperparameter tuning or policy search, where coordinated structure is plausible and evaluations are scarce.
The rate gain relative to the curse of dimensionality suggests the method will show its largest advantage in high-dimensional problems, making BOMM a candidate of choice when dimension is large but the run budget is tiny.
A testable extension would be replacing the assumed link function with a learned nonparametric link, which could relax the modeling assumption while keeping the marginal-means machinery intact.
The theory implicitly suggests a budget-allocation heuristic: spend runs on estimating marginals across coordinates rather than concentrating on local search around the current best point.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things to know. First, the idea in the abstract is genuinely interesting: instead of pick-the-winner, estimate marginal mean functions and use them to propose candidates outside the evaluated set. If that works, it is a real step for high-dimensional expensive black-box optimization. Second, the full text attached to arXiv:2508.01834 is not this paper. It is “Large Kernel MedNeXt”, a breast MRI segmentation paper. So as submitted, there is no proof, no assumptions, no experiments, and no code for BOMM. The mismatch is mechanical, not a judgment about the authors, but it makes review impossible.

What I can fairly credit from the abstract: the marginal-mean estimator is a substantive departure from the standard pick-the-winner solution; the claim of a consistency result and an optimization rate that “tempers” the curse of dimensionality is precisely the kind of theory the field needs; and the proposed practical framework using a transformed additive Gaussian process is concrete. The neutrino detector application is appropriate and not a trivial test problem.

The soft spots are mostly consequences of the missing text. The theorem is stated but not available, so “mild conditions” cannot be examined. The rate claim could mean many things; without the proof we cannot tell whether the rate is genuinely better in dimension or just a restatement. The biggest substantive assumption, visible even from the abstract, is that the objective is a generalized additive model with unknown link. For a real neutrino detector simulator that is a strong structural assumption, and the paper would need to say how severely performance degrades when additivity fails. That is a fair empirical question, not a fatal flaw.

If the actual BOMM manuscript exists and contains the promised proof, code, and experiments, it deserves a serious referee: the idea is important and the theory is checkable. The intended reader would be someone in Bayesian optimization or computer experiments with expensive simulators. But the version I was given is unreviewable. I would send it back for the correct full text before any referee sees it.

Referee Report

3 major / 2 minor

Summary. The abstract of arXiv:2508.01834 presents a new method, Black-box Optimization via Marginal Means (BOMM), for optimizing expensive black-box simulators, with claimed theoretical guarantees of consistency and an optimization rate that tempers the curse of dimensionality under a generalized additive model with unknown link function, plus a practical implementation using a transformed additive Gaussian process and an application to neutrino detector optimization. The full text supplied for the manuscript, however, is a completely unrelated paper titled "Large Kernel MedNeXt for Breast Tumor Segmentation and Self-Normalizing Network for pCR Classification in Magnetic Resonance Images" by Toufiq Musah, which addresses DCE-MRI breast tumor segmentation and pathological complete response classification. This full text contains no mention of BOMM, marginal means, black-box optimization, additive models, or neutrino detectors, and it provides none of the claimed theorems, proofs, algorithms, numerical experiments, or application results. As submitted, the manuscript does not contain the contribution announced in its abstract.

Significance. The claims in the abstract are potentially significant in the field of expensive black-box optimization: a consistent estimator that goes beyond the evaluated set and an optimization rate that tempers dimensional dependence would be valuable for simulator-based design problems. The abstract's idea of using marginal mean functions under an additive model is plausible and worth investigating. However, because the full text is a different paper, the manuscript provides no derivations, no theorem statements, no empirical evidence, and no code for the BOMM method. Thus the significance cannot be assessed on the merits; the submission as it stands fails to establish any of its stated contributions. No credit can be given for machine-checked proofs, reproducible code, or falsifiable predictions, since none are present in the submitted full text.

major comments (3)

[Full text] The complete text of the manuscript is the paper "Large Kernel MedNeXt for Breast Tumor Segmentation and Self-Normalizing Network for pCR Classification in Magnetic Resonance Images," which is about medical image analysis and contains no discussion of black-box optimization, marginal means, additive Gaussian processes, or neutrino detectors; the abstract's central claims are therefore unsupported by any body of the paper.
[Abstract] The abstract asserts that "we prove that the BOMM estimator not only is consistent for optimization, but also has an optimization rate that tempers the curse-of-dimensionality," yet the full text contains no theorem, proof, or even a statement of the "mild conditions" referenced in the abstract; the reader cannot verify the hypotheses or the claimed rate, so the central theoretical result is unverifiable.
[Full text] The abstract announces a practical framework based on a "transformed additive Gaussian process surrogate model" and numerical experiments including a neutrino detector application, but none of these elements appear in the full text; the submitted paper contains no algorithm description, no experimental setup, no results tables, and its code link points to a medical imaging repository, making the claimed empirical demonstration absent.

minor comments (2)

[References] The reference list in the full text contains only medical imaging citations and does not include any prior work on marginal means, additive Gaussian processes, or high-dimensional black-box optimization, so the manuscript lacks even the bibliographic grounding for the claimed method.
[Abstract] The abstract introduces the terms "BOMM estimator" and "transformed additive Gaussian process surrogate model" without definitions, and the full text never defines them; the manuscript is internally incomplete as a self-contained paper.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity is evidenced from the available material; the supplied full text is an unrelated paper, so the BOMM proof cannot be examined, but absence of proof is a verification gap, not circularity.

full rationale

The abstract claims a new estimator 'BOMM' that uses marginal mean functions and states a theorem under a generalized additive model assumption: 'Assuming the objective function follows a generalized additive model with unknown link function and under mild conditions, we prove that the BOMM estimator not only is consistent for optimization, but also has an optimization rate that tempers the curse-of-dimensionality.' This claim is not visibly circular: the target x* is an external object, the estimator is built from marginal means, and the theorem is stated as a mathematical result to be proven. However, the full text submitted for arXiv:2508.01834 is actually 'Large Kernel MedNeXt for Breast Tumor Segmentation and Self-Normalizing Network for pCR Classification in Magnetic Resonance Images', a medical-imaging paper with no mention of BOMM, marginal means, black-box optimization, or neutrino detectors. Consequently, the derivation chain and the precise 'mild conditions' cannot be inspected. This is a verification gap rather than an identified circular step: I cannot quote any equation in which the BOMM estimator is defined in terms of the optimizer it claims to estimate, nor any fitted parameter that is renamed as a prediction, nor any load-bearing self-citation chain. Without such quoted evidence, the rules require a non-finding. The honest assessment is that the paper's central mathematical content is absent from the supplied text, so no circularity can be confirmed.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

The abstract's central theorem rests on the generalized additive model assumption and on unspecified mild conditions. No explicit free parameters or invented physical entities are stated in the abstract. The practical surrogate's hyperparameters and link function are not described, so a full ledger is impossible without the actual manuscript.

assumptions (2)

domain assumption The black-box objective function follows a generalized additive model with unknown link function.
This is the central modeling assumption under which the BOMM consistency and rate theorem is proved in the abstract. If the real simulator has strong interactions or is far from additive, the guarantee does not apply.
ad hoc to paper There exist unspecified 'mild conditions' on the simulator, inputs, and estimation procedure that make the marginal mean functions efficiently inferable.
The abstract invokes these conditions without stating them. They are load-bearing for the claimed dimension-tempering rate, since the practical usefulness of BOMM depends on being able to estimate the marginal means from limited runs.

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Cite this review

Pith. "Pith review of Efficient optimization of expensive black-box simulators via marginal means, with application to neutrino detector design." pith.science (2026). https://pith.science/paper/EC2JAGUI

@misc{pith2026250801834,
  author       = {Pith},
  title        = {Pith review of: Efficient optimization of expensive black-box simulators via marginal means, with application to neutrino detector design},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EC2JAGUI}},
  note         = {Machine review of arXiv:2508.01834}
}

abstract

With advances in scientific computing, computer experiments are increasingly used for optimizing complex systems. However, for modern applications, e.g., the optimization of nuclear physics detectors, each experiment run can require hundreds of CPU hours, making the optimization of its black-box simulator over a high-dimensional space a challenging task. Given limited runs at inputs $\mathbf{x}_1, \cdots, \mathbf{x}_n$, the best solution from these evaluated inputs can be far from optimal, particularly as dimensionality increases. Existing black-box methods, however, largely employ this ''pick-the-winner'' (PW) solution, which leads to mediocre optimization performance. To address this, we propose a new Black-box Optimization via Marginal Means (BOMM) approach. The key idea is a new estimator of a global optimizer $\mathbf{x}^*$ that leverages the so-called marginal mean functions, which can be efficiently inferred with limited runs in high dimensions. Unlike PW, this estimator can select solutions beyond evaluated inputs for improved optimization performance. Assuming the objective function follows a generalized additive model with unknown link function and under mild conditions, we prove that the BOMM estimator not only is consistent for optimization, but also has an optimization rate that tempers the ''curse-of-dimensionality'' faced by existing methods, thus enabling better performance as dimensionality increases. We present a practical framework for implementing BOMM using the transformed additive Gaussian process surrogate model. Finally, we demonstrate the effectiveness of BOMM in numerical experiments and an application on neutrino detector optimization in nuclear physics.

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Reviewed August 6, 2026 · model on record in the stance chip above.

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