Conservative quantum offline model-based optimization

Annie E. Paine; Antonio A. Gentile; Kristian Sotirov; Osvaldo Simeone; Savvas Varsamopoulos

arxiv: 2506.19714 · v2 · submitted 2025-06-24 · 🪐 quant-ph · cs.LG· stat.ML

Conservative quantum offline model-based optimization

Kristian Sotirov , Annie E. Paine , Savvas Varsamopoulos , Antonio A. Gentile , Osvaldo Simeone This is my paper

Pith reviewed 2026-05-19 07:43 UTC · model grok-4.3

classification 🪐 quant-ph cs.LGstat.ML

keywords offline model-based optimizationquantum extremal learningconservative objective modelsvariational quantum circuitsblack-box optimizationsurrogate modelingout-of-distribution regularization

0 comments

The pith

Integrating conservative regularization into quantum extremal learning produces higher-value solutions for offline black-box optimization.

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

The paper proposes COM-QEL to combine variational quantum circuits, which learn surrogate functions from limited input-output data, with conservative objective models that penalize overly optimistic predictions on inputs far from the training set. This targets the problem of offline model-based optimization, where active experimentation is impossible and standard models often extrapolate incorrectly to suggest invalid high-objective designs. By adding regularization for caution on out-of-distribution points while retaining quantum expressivity, the method aims to select proposals that actually perform better when evaluated on the true objective. Benchmark experiments show COM-QEL consistently outperforms plain QEL in recovering higher true objective values.

Core claim

The authors claim that embedding conservative objective models into quantum extremal learning yields a hybrid algorithm that exploits the modeling capacity of variational quantum circuits yet reliably avoids selecting over-optimistic candidates outside the observed data distribution, resulting in superior performance on standard offline optimization benchmarks.

What carries the argument

The COM-QEL hybrid that applies conservative regularization to the output of a variational quantum circuit trained as a surrogate model.

If this is right

COM-QEL can be run on existing offline datasets to generate design candidates with higher verified objective values than those from plain QEL.
The regularization step limits extrapolation errors that would otherwise cause selection of invalid high-scoring points.
The approach preserves the data efficiency of quantum surrogate learning while adding a safeguard for generalization.
Empirical gains appear across multiple benchmark optimization tasks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Similar conservative penalties could be tested on other variational quantum models used for regression or generation tasks.
The method might reduce the number of follow-up experiments needed when moving from offline proposals to laboratory validation.
If the conservative term can be tuned automatically, the framework could extend to larger quantum circuit depths without additional classical post-processing.

Load-bearing premise

Conservative objective models can be added to variational quantum circuits without destroying their ability to fit the training data while still producing reliably cautious predictions on unseen inputs.

What would settle it

An experiment on a benchmark task in which a solution proposed by COM-QEL has a lower true objective value than one proposed by standard QEL.

Figures

Figures reproduced from arXiv: 2506.19714 by Annie E. Paine, Antonio A. Gentile, Kristian Sotirov, Osvaldo Simeone, Savvas Varsamopoulos.

**Figure 2.** Figure 2: Usefulness (top) and novelty (bottom) for classical COM [8], [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** Figure 4: Usefulness (top) and novelty (bottom) for classical COM [8], [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

read the original abstract

Offline model-based optimization (MBO) refers to the task of optimizing a black-box objective function using only a fixed set of prior input-output data, without any active experimentation. Recent work has introduced quantum extremal learning (QEL), which leverages the expressive power of variational quantum circuits to learn accurate surrogate functions by training on a few data points. However, as widely studied in the classical machine learning literature, predictive models may incorrectly extrapolate objective values in unexplored regions, leading to the selection of overly optimistic solutions. In this paper, we propose integrating QEL with conservative objective models (COM) - a regularization technique aimed at ensuring cautious predictions on out-of-distribution inputs. The resulting hybrid algorithm, COM-QEL, builds on the expressive power of quantum neural networks while safeguarding generalization via conservative modeling. Empirical results on benchmark optimization tasks demonstrate that COM-QEL reliably finds solutions with higher true objective values compared to the original QEL, validating its superiority for offline design problems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

COM-QEL adds a classical conservative regularizer to QEL and reports better benchmark performance, but the details and quantum-specific safeguards are thin.

read the letter

The main takeaway is that this paper combines quantum extremal learning with conservative objective modeling to reduce over-optimistic predictions in offline optimization. The hybrid, called COM-QEL, applies a regularization penalty drawn from classical work to keep the surrogate cautious outside the training data, and the authors show it selects points with higher true objective values than plain QEL on their benchmarks. That integration is the concrete step forward. It takes an existing quantum surrogate approach and layers on a known classical fix without inventing new machinery, which keeps the method practical for data-scarce design tasks. The reported gains on the benchmarks are the part that could interest people already running QEL experiments. The soft spots are the missing specifics and the unaddressed quantum wrinkle. The abstract gives no dataset sizes, no circuit depths or qubit counts, no regularization strengths, and no mention of statistical tests or controls for multiple runs. Without those, the empirical edge is hard to judge as robust. More critically, the conservative term is a classical additive penalty, yet the surrogate is a variational circuit whose feature map lives in a high-dimensional space with non-convex training. Nothing in the work derives a bound or runs a targeted check showing the penalty actually suppresses optimistic extrapolation once circuit depth grows. That gap matches the concern that the safeguard may not transfer cleanly. This is for researchers working on quantum surrogates for offline model-based optimization, especially those already familiar with QEL or classical conservative methods. A reader in that niche can extract the hybrid idea and try it, but the paper is not aimed at a broader audience. It deserves peer review so the methods section, full experimental controls, and any additional analysis can be examined directly.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces COM-QEL, which augments quantum extremal learning (QEL) based on variational quantum circuits with conservative objective models (COM) to reduce over-optimistic extrapolations on out-of-distribution inputs in offline model-based optimization. The central empirical claim is that COM-QEL identifies solutions with higher true objective values than standard QEL on benchmark tasks.

Significance. If the empirical superiority is confirmed with proper statistical controls and the conservative property is shown to hold for quantum feature maps, the approach would usefully extend classical regularization techniques to quantum surrogate models for offline design problems.

major comments (2)

[Abstract] Abstract: the claim that COM-QEL 'reliably finds solutions with higher true objective values' is presented without any reported dataset sizes, circuit depths, regularization strengths, number of trials, or statistical significance tests, leaving the central empirical claim unsupported.
[Method] Method description: no derivation or bound is given showing that the added conservative penalty continues to suppress optimistic extrapolations once the surrogate is realized by a variational quantum circuit whose output is a non-linear function of a high-dimensional quantum feature map; the skeptic concern that the regularizer may be satisfied while OOD values remain inflated is therefore unaddressed.

minor comments (2)

Define all acronyms (QEL, COM, MBO) at first use and ensure consistent notation for the conservative penalty term across equations.
Add a table or figure caption that explicitly lists the benchmark tasks, input dimensions, and offline dataset cardinalities used in the experiments.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and indicate where revisions will be made to improve clarity and support for our claims.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that COM-QEL 'reliably finds solutions with higher true objective values' is presented without any reported dataset sizes, circuit depths, regularization strengths, number of trials, or statistical significance tests, leaving the central empirical claim unsupported.

Authors: We agree that the abstract, as a concise summary, omits specific experimental parameters. These details—including dataset sizes, circuit depths, regularization strengths, number of trials, and statistical significance tests—are reported in the Experiments section of the full manuscript. To address the concern directly, we will revise the abstract to briefly reference the key experimental settings and note that statistical validation is provided in the main text. revision: yes
Referee: [Method] Method description: no derivation or bound is given showing that the added conservative penalty continues to suppress optimistic extrapolations once the surrogate is realized by a variational quantum circuit whose output is a non-linear function of a high-dimensional quantum feature map; the skeptic concern that the regularizer may be satisfied while OOD values remain inflated is therefore unaddressed.

Authors: The conservative penalty is applied to the scalar output of the surrogate model after the quantum feature map and measurement. We will add a paragraph in the revised Methods section clarifying that the penalty operates on this final scalar prediction in the same way as in the classical COM formulation, independent of the internal non-linear quantum representation. We will also include additional empirical results showing suppressed OOD predictions. However, a formal derivation or bound specific to variational quantum circuits is not provided in the manuscript. revision: partial

standing simulated objections not resolved

No derivation or bound is given showing that the added conservative penalty continues to suppress optimistic extrapolations for variational quantum circuits.

Circularity Check

0 steps flagged

No significant circularity; method augments QEL with external regularization and validates empirically

full rationale

The paper defines COM-QEL by integrating an external conservative regularization technique with the existing QEL baseline. The central claim of superior performance rests on new empirical results from benchmark tasks rather than any derivation that reduces by construction to fitted parameters, self-citations, or ansatzes internal to the model. No load-bearing step equates a prediction to its own input or relies on a uniqueness theorem imported from overlapping prior work. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach rests on standard domain assumptions from quantum machine learning and classical conservative regularization; no free parameters or invented entities are described in the abstract.

axioms (2)

domain assumption Variational quantum circuits can serve as expressive surrogate models for black-box objectives when trained on limited data.
This underpins the QEL component referenced in the abstract.
domain assumption Conservative objective models can be applied to quantum circuits without destroying their learning capability.
This is the key integration premise needed for the hybrid to work.

pith-pipeline@v0.9.0 · 5706 in / 1309 out tokens · 57262 ms · 2026-05-19T07:43:02.308366+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

COM-QEL addresses the constrained problem θCOM-QEL = arg min ... s.t. 1/N Σ fθ(xθ,T(xi)) − 1/N Σ fθ(xi) ≤ τ
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

PQC surrogate fθ(x) = ⟨0|U†θ(x) M Uθ(x)|0⟩ optimized by parameter-shift rules

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages · 1 internal anchor

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Offline Model-Based Optimization: Compre- hensive Review

M. Kim, J. Gu, Y . Yuan, T. Yun, Z. Liu, Y . Bengio, and C. Chen. “Offline Model-Based Optimization: Compre- hensive Review” (2025). arXiv: 2503.17286

work page arXiv 2025

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Conditioning by adaptive sampling for robust design

D. Brookes, H. Park, and J. Listgarten. “Conditioning by adaptive sampling for robust design”. In: Proceed- ings of the 36th International Conference on Machine Learning. Ed. by K. Chaudhuri and R. Salakhutdinov. V ol. 97. Proceedings of Machine Learning Research. pp. 773–782., Sept. 2019, pp. 773–782

work page 2019

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Geometric programming for aircraft design optimization

W. Hoburg and P. Abbeel. “Geometric programming for aircraft design optimization”. AIAA Journal 52.11 (2014), pp. 2414–2426

work page 2014

[4] [4]

Quantum extremal learning

S. Varsamopoulos, E. Philip, V . Elfving, H. Vlijmen, S. Menon, A. V os, N. Dyubankova, B. Torfs, and A. Rowe. “Quantum extremal learning”. Quantum Machine Intel- ligence 6 (July 2024). DOI: 10.1007/s42484-024-00176- x

work page doi:10.1007/s42484-024-00176- 2024

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O. Simeone. Machine Learning for Engineers . Cam- bridge University Press, 2022

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Schuld and F

M. Schuld and F. Petruccione. Machine Learning with Quantum Computers . Quantum Science and Technol- ogy. Cham: Springer, 2021. ISBN : 978-3-030-83097-7, 978-3-030-83100-4, 978-3-030-83098-4. DOI: 10.1007/ 978-3-030-83098-4

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An introduction to quantum machine learning for engineers

O. Simeone. “An introduction to quantum machine learning for engineers”. Foundations and Trends® in Signal Processing 16.1-2 (2022), pp. 1–223

work page 2022

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Conservative Objective Models for Effective Offline Model-Based Optimization

B. Trabucco, A. Kumar, X. Geng, and S. Levine. “Conservative Objective Models for Effective Offline Model-Based Optimization”. In: Proceedings of the 38th International Conference on Machine Learning . Ed. by M. Meila and T. Zhang. V ol. 139. Proceedings of Machine Learning Research. PMLR, 18-24 Jul 2021, pp. 10358–10368

work page 2021

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Roma: Robust model adaptation for offline model-based optimization

S. Yu, S. Ahn, L. Song, and J. Shin. “Roma: Robust model adaptation for offline model-based optimization”. Advances in Neural Information Processing Systems 34 (2021), pp. 4619–4631

work page 2021

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Data-driven of- fline decision-making via invariant representation learn- ing

H. Qi, Y . Su, A. Kumar, and S. Levine. “Data-driven of- fline decision-making via invariant representation learn- ing”. Advances in Neural Information Processing Sys- tems 35 (2022), pp. 13226–13237

work page 2022

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Incorporating Surrogate Gradient Norm to Improve Offline Optimization Techniques

C. Dao, P. L. Nguyen, T. Thao Nguyen, and N. Hoang. “Incorporating Surrogate Gradient Norm to Improve Offline Optimization Techniques”. Advances in Neural Information Processing Systems 37 (2024), pp. 8014– 8046

work page 2024

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Practi- cal Bayesian Optimization of Machine Learning Algo- rithms

J. Snoek, H. Larochelle, and R. P. Adams. “Practi- cal Bayesian Optimization of Machine Learning Algo- rithms”. In: Advances in Neural Information Processing Systems. Ed. by F. Pereira, C. Burges, L. Bottou, and K. Weinberger. V ol. 25. Curran Associates, Inc., 2012

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Conditional Neural Processes

M. Garnelo, D. Rosenbaum, C. Maddison, T. Ramalho, D. Saxton, M. Shanahan, Y . W. Teh, D. Rezende, and S. M. A. Eslami. “Conditional Neural Processes”. In: Proceedings of the 35th International Conference on Machine Learning. Ed. by J. Dy and A. Krause. V ol. 80. Proceedings of Machine Learning Research. PMLR, Oct. 2018, pp. 1704–1713

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Model inversion networks for model-based optimization

A. Kumar and S. Levine. “Model inversion networks for model-based optimization”. Advances in neural infor- mation processing systems 33 (2020), pp. 5126–5137

work page 2020

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Functional graphical models: Structure enables offline data-driven optimization

K. Grudzien, M. Uehara, S. Levine, and P. Abbeel. “Functional graphical models: Structure enables offline data-driven optimization”. In: International Conference on Artificial Intelligence and Statistics . PMLR. 2024, pp. 2449–2457

work page 2024

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arXiv preprint arXiv:1909.12264 (2019)

G. Verdon, T. McCourt, E. Luzhnica, V . Singh, S. Leichenauer, and J. Hidary. “Quantum graph neural networks”. arXiv preprint arXiv:1909.12264 (2019)

work page arXiv 1909

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Effect of data encoding on the expressive power of variational quantum-machine-learning models

M. Schuld, R. Sweke, and J. J. Meyer. “Effect of data encoding on the expressive power of variational quantum-machine-learning models”. Phys. Rev. A 103 (3 Mar. 2021), p. 032430. DOI: 10 . 1103 / PhysRevA . 103.032430

work page 2021

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Quantum circuit learning,

K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii. “Quantum circuit learning”. Phys. Rev. A 98 (3 Sept. 2018), p. 032309. DOI: 10.1103/PhysRevA.98.032309

work page doi:10.1103/physreva.98.032309 2018

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Evaluating analytic gradients on quantum hardware,

M. Schuld, V . Bergholm, C. Gogolin, J. Izaac, and N. Killoran. “Evaluating analytic gradients on quantum hardware”. Phys. Rev. A 99 (3 Mar. 2019), p. 032331. DOI: 10.1103/PhysRevA.99.032331

work page doi:10.1103/physreva.99.032331 2019

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Con- vergence error analysis of reflected gradient Langevin dynamics for non-convex constrained optimization

K. Sato, A. Takeda, R. Kawai, and T. Suzuki. “Con- vergence error analysis of reflected gradient Langevin dynamics for non-convex constrained optimization”. Japan Journal of Industrial and Applied Mathematics 42.1 (2025), pp. 127–151

work page 2025

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Primal-dual subgradient methods for convex problems

Y . Nesterov. “Primal-dual subgradient methods for convex problems”. Mathematical programming 120.1 (2009), pp. 221–259

work page 2009

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D. P. Kingma and J. Ba. Adam: A Method for Stochastic Optimization. 2017. arXiv: 1412.6980 [cs.LG]

work page internal anchor Pith review Pith/arXiv arXiv 2017

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Hardware- efficient variational quantum eigensolver for small molecules and quantum magnets

A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta. “Hardware- efficient variational quantum eigensolver for small molecules and quantum magnets”. Nature 549.7671 (Sept. 2017), pp. 242–246. ISSN : 1476-4687. DOI: 10. 1038/nature23879

work page 2017

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M. A. Nielsen and I. L. Chuang. Quantum computation and quantum information . Cambridge University Press, 2010

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Solv- ing nonlinear differential equations with differentiable quantum circuits

O. Kyriienko, A. E. Paine, and V . E. Elfving. “Solv- ing nonlinear differential equations with differentiable quantum circuits”. Physical Review A 103.5 (2021), p. 052416

work page 2021

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Classical versus quantum models in machine learning: insights from a finance application

J. Alcazar, V . Leyton-Ortega, and A. Perdomo-Ortiz. “Classical versus quantum models in machine learning: insights from a finance application”. Machine Learning: Science and Technology 1.3 (2020), p. 035003

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J. Kim. Benchmark functions for bayesian optimization. 2020

work page 2020