Robust and Adaptive Optimization under a Large Language Model Lens

Dimitris Bertsimas; Georgios Margaritis

REVIEW 3 major objections 4 minor 3 cited by

Robust and Adaptive Optimization under a Large Language Model Lens

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read With tailored prompts, ChatGPT can reformulate simple robust optimization problems into solvable code.

desk verdict First LLM-for-RO/ARO proof-of-concept with honest failure examples, but the 'little to no errors' claim is unquantified and the evidence is anecdotal. read the letter →

arxiv 2501.00568 v1 pith:HPVZUZ65 submitted 2024-12-31 math.OC

Dimitris Bertsimas , Georgios Margaritis This is my paper · ORCID

classification math.OC

keywords robustoptimizationadaptivelargelanguagemodelsChatGPTin-contextlearningpromptengineeringsupportfunctionsformulation

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

Robust and adaptive optimization usually demands a modeling expert who can identify uncertainty sets, apply duality and support-function results, and produce tractable reformulations. This paper claims that ChatGPT, guided by specialized in-context prompts and chain-of-thought instructions, can perform the whole pipeline on simple problems: formulate an optimization problem, add user-specified uncertainty, derive the robust counterpart, and generate executable Julia code. The authors argue the approach works with little to no errors on simple cases, while acknowledging that harder cases and algebraic manipulations can fail. If the claim holds, it would let non-experts apply robust optimization without learning its mathematical toolkit, and would show that large language models can adapt to narrow technical domains through prompt engineering alone.

What carries the argument

The engine of the approach is a set of prompts that package the support-function calculus of robust optimization as rule tables. For a constraint $(a+Pz)^\top x \le b$ with $z$ in an uncertainty set $Z$, the robust counterpart is $a^\top x + \sigma_Z^*(P^\top x) \le b$, where $\sigma_Z^*$ is the conjugate support function of $Z$; the prompts supply closed forms for $p$-norm balls, polyhedral sets, intersections, and Minkowski sums, plus a chain-of-thought instruction to apply them step by step. A second prompt set tells the model how to linearize $\ell_1$ and $\ell_\infty$ norms and to model $\ell_2$ norms with second-order cone constraints when writing solver code. For adaptive robust optimization, the prompts introduce the linear decision rule $y(z)=v+Uz$, which converts an adjustable constraint into a standard robust constraint with the same support-function machinery. The entire method is the combination of these rule tables with in-context learning, not any new optimization theory.

What would settle it

Run the paper's prompting pipeline on a fixed benchmark of, say, one hundred simple robust linear programs (a few variables, one or two constraints, standard uncertainty sets such as $\ell_1$, $\ell_2$, $\ell_\infty$, and polyhedral), execute the generated Julia code, and compare each robust counterpart against a reference derivation; the central claim weakens if more than a small fraction of simple cases produce an incorrect robust counterpart or fail to run.

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Extended reading notes

Core claim

The paper's central demonstration is that a general-purpose chatbot, given a small set of informational prompts encoding the vocabulary of robust and adaptive optimization, can act as an automatic RO/ARO modeler. In the worked examples, ChatGPT correctly converts a constraint of the form $(a+Pz)^\top x \le b$ into its tractable robust counterpart $a^\top x + \sigma_Z^*(P^\top x) \le b$ for choices such as $p$-norm and polyhedral uncertainty sets, correctly handles constraints given in $\ge$ form by flipping signs, combines uncertainty sets in some cases, and writes executable Julia code that linearizes $\ell_1$ and $\ell_\infty$ norms and models $\ell_2$ norms via second-order cones. For adaptive problems, it formulates wait-and-see decisions under a linear decision rule $y(z)=v+Uz$, takes the robust counterpart of the resulting single-stage problem, and even extrapolates to a quadratic decision rule. The paper also documents failures: inconsistent answers across runs, algebraic rearrangement errors, and using the Minkowski-sum rule instead of the intersection rule when combining uncertainty sets. The overall claim is that in-context learning plus chain-of-thought prompting is sufficient adaptation to this niche domain, even though ChatGPT without those prompts performs poorly out of the box.

Load-bearing premise

The demonstrations are a small selection of conversations, and the paper reports no systematic measurements of how often the pipeline succeeds, so the 'little to no errors' claim rests on the authors' informal observation of a few successful runs.

Editorial extensions

If this is right

Non-expert users could describe a problem in plain language and receive a robust model with executable code, without learning support functions or duality theory.
The prompting scheme could be used as an interactive teaching aid for robust and adaptive optimization, since ChatGPT walks through each reformulation step.
If the method generalizes, simple RO/ARO projects that currently require a modeling specialist could be automated, lowering the cost of adding robustness.
For adaptive problems, the same prompts let the model handle here-and-now versus wait-and-see variables under linear decision rules, a key class of practical dynamic problems.
Because the model can extrapolate to quadratic decision rules from a linear-rule example, the approach may extend to richer decision-rule families without new prompts.

Reading between the lines

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

A systematic benchmark would likely show that success rates drop sharply as problem size or uncertainty-set complexity grows; the paper's examples are small and hand-picked.
The hybrid pattern suggested here—LLM generates, a solver or symbolic engine verifies—could make the approach reliable enough for real use; the paper itself stops at standalone prompting.
The same prompt-encoding strategy could be applied to other transformation-heavy fields, such as conic duality, stochastic programming reformulations, or integer-programming cuts, where a compact rule table is the key bottleneck for non-experts.

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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

Quick take: this is the first paper I know of that pushes ChatGPT into robust and adaptive robust optimization specifically, and the authors are honest enough to show failures. The new bit is the domain application: NL4OPT and Tsouros et al. did general optimization or constraint modeling, but nobody had demonstrated the full robust-counterpart pipeline via in-context prompting. The prompts are printed in full, so the method is reproducible, and the examples are genuinely instructive—ChatGPT handling the >= to <= flip, different uncertainty sets per constraint, linear decision rules, and even extrapolating to a quadratic decision rule.

The soft spot is the central claim. The abstract and intro say ChatGPT performs these steps with "little to no errors" for simple problems, but there is no test set, no sampling rule, no error count. Section 3 then shows the model tripping on simple algebra (100x1 + x2 >= 10 + x1 becomes a = [-99, 1] instead of [-99, -1]) and confusing Minkowski sum with intersection when combining uncertainty sets. Those are exactly the simple settings the claim is about. So the successes in Section 2 cannot be read as representative without a defined test distribution and measured pass rates. The stress-test note is right on this.

Also, the prompts hand the model the transformation rules, so the demonstration shows the model can apply rules it is given, not that it discovered RO. That is fine for a proof-of-concept, but it lowers the wow factor. The paper itself acknowledges this indirectly by saying ChatGPT performs poorly out-of-the-box.

Who is this for: people working on LLMs for operations research, and readers curious whether ChatGPT can be scaffolded into niche domains with heavy prompting. It is a proof-of-concept, not a benchmark. As an IJOC paper it is light; as a workshop paper or a first study it is fine.

Recommendation: send it to peer review, but the referee should require systematic evaluation—a defined problem distribution, pass rates, and an error taxonomy—before the "little to no errors" claim can stand. If the authors reframe the contribution as "ChatGPT can do this with substantial scaffolding, and here are the failure modes," it is a decent contribution.

Referee Report

3 major / 4 minor

Summary. The paper reports a proof-of-concept study in which ChatGPT 3.5, guided by specialized informational prompts and chain-of-thought prompting, is used to automate parts of the Robust Optimization (RO) and Adaptive Robust Optimization (ARO) modeling pipeline: problem formulation, introduction of uncertainty, derivation of the robust counterpart, and generation of executable Julia code. The authors present four worked example conversations, describe the prompts they designed, and then list limitations including inconsistency, algebraic errors, and incorrect application of theorems. The paper's title and abstract claim that, for simple problems, ChatGPT performs these steps 'with little to no errors,' while later sections acknowledge concrete failures on equally simple inputs.

Significance. If the central claim were rigorously established, the paper would provide a useful demonstration that LLMs can be steered into a niche technical domain through in-context prompting, potentially lowering the barrier to using RO/ARO. The authors are transparent about their failures and about the stochastic nature of the model, and they give a clear description of the prompting recipe, which is a useful starting point for further work. However, the evidence is anecdotal: there is no systematic test set, no error rate, no baseline comparison, and no reproducibility protocol. These omissions are load-bearing because the contribution rests on the reliability of the claimed capability, not on the mathematical correctness of the background material, which is standard. The paper is best read as a qualitative demonstration; in its current form the empirical core is unverified.

major comments (3)

[Abstract; §2.1.2 and §2.2.2] The abstract's claim that ChatGPT performs the RO/ARO steps 'with little to no errors' is not supported by any quantitative evidence. No test set, sampling rule, scoring rubric, or error count is given. Section 3 itself reports concrete errors on simple inputs: the constraint 100x1 + x2 >= 10 + x1 is rearranged to a = [-99, 1] instead of the correct [-99, -1], and the robust counterpart for the intersection of a 2-norm ball and an infinity-norm ball is incorrectly derived using the Minkowski-sum property rather than the intersection rule with auxiliary variables w1 and w2. These are precisely the simple settings to which the abstract's claim refers. The authors should either conduct a systematic evaluation with defined pass/fail criteria or substantially qualify the claim.
[§1.1, §1.2, §2.1.2] The paper asserts that ChatGPT performs 'very poorly out-of-the-box' on RO and ARO and that the proposed in-context prompting is what enables the demonstrated behavior, but no baseline is reported. The reader cannot determine whether the successes are due to the prompts, to the model's general capabilities, or to the particular examples chosen. To support the adaptation claim, the authors should run the same tasks without the specialized prompts (e.g., the same user queries with no appended Prompt 2.1-2.6) and report both outcomes.
[§2 and §3] The demonstration is not reproducible as reported. The examples in §2 appear to be selected successful conversations, but the selection criterion is not stated, and no version/date of ChatGPT, temperature setting, number of repeated runs, or failure counts are provided. Section 3 itself notes that identical prompts yield different responses, so a single transcript is not a stable artifact. For an INFORMS Journal on Computing submission, the authors should specify the model version and sampling parameters, run each example multiple times, and provide transcripts or a public repository with the prompts and generated code.

minor comments (4)

[Abstract; title page] The abstract contains the typo 'higlhy' for 'highly', and 'Massachussetts' appears in the author affiliations; these should be corrected.
[§2.1.1, Eq. (11)] In Eq. (11), the dual norm notation ||P x||_E with E = D/(D-1) is introduced without explaining that this is the dual norm of the original D-norm ball; this should be stated explicitly.
[Prompt 2.3 and Prompt 2.6] The phrase 'conjugate of the support function' is a misnomer: the quantity δ*(x|Z) is the support function of Z, i.e., the conjugate of the indicator function of Z. This terminology should be corrected, since the prompts are a key part of the method and accuracy of mathematical language matters.
[§3, 'Applying mathematical theorems' example] The user prompt contains the typo '≤=' instead of '≤'; also, when describing the correct intersection robust counterpart, the auxiliary-variable constraint w1 + w2 = P^T x is only mentioned in prose and not displayed in the final corrected form, which would improve clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the RO/ARO transformation rules are supplied as prompts by design, so the demonstrations test in-context application rather than independent derivation.

full rationale

The paper's contribution is an empirical demonstration of in-context learning: with prompts that explicitly state the RO/ARO reformulation rules (Prompts 2.1–2.6), ChatGPT can formulate problems, introduce uncertainty, write the robust counterpart, and produce Julia code. Because the prompting scheme is the method, the fact that the outputs use the supplied rules is not a hidden reduction; the paper never claims ChatGPT discovers the support-function conjugates from first principles. The Section 3 failure examples (wrong rearrangement of 100x1+x2>=10+x1, Minkowski-sum instead of intersection for Z1∩Z2, inconsistent responses to identical prompts) show the outputs are not logically forced by the prompts, so the demonstration has independent empirical content. The repeated citations to Bertsimas and Den Hertog (2022), a textbook co-authored by the first author, supply standard, externally checkable RO results that form the prompt content; they are not load-bearing for the LLM-capability claim. The unquantified 'little to no errors' statement and lack of a systematic evaluation are evidence-quality concerns, not circularity, and do not raise the circularity score.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new parameters or entities. It relies on standard robust optimization theory and on the assumption that the selected ChatGPT interactions are representative.

assumptions (3)

standard math The support function conjugates and robust counterpart transformations from Bertsimas and Den Hertog (2022) are correct and applicable.
The paper relies on these results in the prompts and in the background sections.
domain assumption The examples shown are representative of typical ChatGPT performance on simple RO/ARO problems.
No systematic evaluation is provided; the paper's claim of 'little to no errors' depends on this assumption.
domain assumption ChatGPT 3.5 behaves similarly across different runs and for different users.
The paper discusses non-determinism in the limitations, so the reproducibility of the demonstrations is questionable.

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Cite this review

Pith. "Pith review of Robust and Adaptive Optimization under a Large Language Model Lens." pith.science (2026). https://pith.science/paper/HPVZUZ65

@misc{pith2026250100568,
  author       = {Pith},
  title        = {Pith review of: Robust and Adaptive Optimization under a Large Language Model Lens},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HPVZUZ65}},
  note         = {Machine review of arXiv:2501.00568}
}

read the original abstract

In this paper, we explore the application of ChatGPT in the domain of Robust and Adaptive Robust Optimization. We demonstrate that with appropriate prompting, ChatGPT can be used to auto-formulate and solve simple Robust and Adaptive Optimization Problems. We first develop specialized informational prompts tailored to the domains of Adaptive and Robust Optimization. Then, we show that using these prompts, ChatGPT is able to (i) formulate an optimization problem, (ii) adapt the problem so that it accounts for user-specified uncertainty, (iii) derive the computationally tractable robust counterpart of the problem and (iv) produce executable code that solves the problem. For simple Optimization Problems, we show that ChatGPT is able to perform these steps with little to no errors. We also highlight some instances of erroneous execution of the steps. Overall, we show that using in-context learning, ChatGPT has the potential to adapt to higlhy specialized and niche domains, in which it would otherwise demonstrate very poor out-of-the-box performance.

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Forward citations

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Reference graph

Works this paper leans on

17 extracted references · 9 canonical work pages · cited by 3 Pith papers

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, " * write output.state after.block = add.period write newline

ENTRY address author booktitle chapter doi edition editor eid howpublished institution isbn issn journal key month note number organization pages publisher school series title type url volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1...
[2]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in "" FUNCTION format.date year ...
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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

, " * write output.state after.block = add.period write newline

ENTRY address author booktitle chapter doi edition editor eid howpublished institution isbn issn journal key month note number organization pages publisher school series title type url volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1...

[2] [2]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in "" FUNCTION format.date year ...

[3] [3]

European Journal of Operational Research 223(2):295--303, ISSN 0377-2217, ://dx.doi.org/10.1016/j.ejor.2012.05.028

Agatz N, Erera A, Savelsbergh M, Wang X (2012) Optimization for dynamic ride-sharing: A review. European Journal of Operational Research 223(2):295--303, ISSN 0377-2217, ://dx.doi.org/10.1016/j.ejor.2012.05.028

work page doi:10.1016/j.ejor.2012.05.028 2012

[4] [4]

Transportation Science 37(4):368--391, ISSN 0041-1655, ://dx.doi.org/10.1287/trsc.37.4.368.23276

Barnhart C, Belobaba P, Odoni AR (2003) Applications of Operations Research in the Air Transport Industry . Transportation Science 37(4):368--391, ISSN 0041-1655, ://dx.doi.org/10.1287/trsc.37.4.368.23276

work page doi:10.1287/trsc.37.4.368.23276 2003

[5] [5]

SIAM Review 53(3):464--501, ISSN 0036-1445

Bertsimas D, Brown DB, Caramanis C (2011) Theory and Applications of Robust Optimization . SIAM Review 53(3):464--501, ISSN 0036-1445

work page 2011

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https://www.dynamic-ideas.com/books/robust-and-adaptive-optimization

Bertsimas D, Den Hertog D (2022) Robust and Adaptive Optimization . https://www.dynamic-ideas.com/books/robust-and-adaptive-optimization

work page 2022

[7] [7]

Computer Methods in Applied Mechanics and Engineering 196(33):3190--3218, ISSN 0045-7825, ://dx.doi.org/10.1016/j.cma.2007.03.003

Beyer HG, Sendhoff B (2007) Robust optimization -- A comprehensive survey. Computer Methods in Applied Mechanics and Engineering 196(33):3190--3218, ISSN 0045-7825, ://dx.doi.org/10.1016/j.cma.2007.03.003

doi:10.1016/j.cma.2007.03.003 2007

[8] [8]

://dx.doi.org/10.48550/arXiv.1810.04805

Devlin J, Chang MW, Lee K, Toutanova K (2019) BERT : Pre-training of Deep Bidirectional Transformers for Language Understanding . ://dx.doi.org/10.48550/arXiv.1810.04805

arXiv doi:10.48550/arxiv.1810.04805 2019