Writing study: Robust Contextual Optimization with Missing Covariates

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← ICML 2026 oral writing corpus

Qingyuan Xu, Ruiwei Jiang · Official ICML 2026 oral record

Observed writing choices, not acceptance rules. This study examines the inspected manuscript version. It does not establish why the paper was accepted or that its presentation choices should be copied unchanged.

Figure, table and section ledger

Editorial contribution type: Theory & formal analysis (primary).

Layout extraction, not a required paper template. Counts are distinct caption labels; a multi-panel figure counts once. Section spans are estimated from heading positions, including floats and whitespace. Method and limitations.

Canonical PDF

62 physical pages

Before references / appendix

≈ 9.16 page-equivalents

Main figures / tables

6 / 2

Attached appendix figures / tables

3 / 5

Attached appendix span

≈ 50.91 page-equivalents

Before references / appendix: ≈ 14.77%References / intervening material: ≈ 3.11%Attached appendix: ≈ 82.11%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Section-by-section lengths and source pages

The title/abstract/front matter precede the first numbered heading. A span ends at the next detected top-level heading, not at the last sentence; end-page whitespace is included. References and statements are listed separately. These are not measurements of text-only or artwork area.

Top-level heading	Starts on PDF page	Estimated span	Share of entire PDF
1. Introduction	1	≈ 1.08 pp.	1.74%
2. A Unified Model	2	≈ 1.74 pp.	2.81%
3. Tractable Reformulations and Statistical	4	≈ 3.93 pp.	6.34%
4. Numerical Experiments	8	≈ 1.96 pp.	3.16%
Impact Statement	10	≈ 0.08 pp.	0.13%
Acknowledgements	10	≈ 0.05 pp.	0.08%
References	10	≈ 1.92 pp.	3.1%
A. Notations	12	≈ 1 pp.	1.61%
B. Additional Literature Review	13	≈ 2 pp.	3.23%
C. Technical Proofs	15	≈ 35 pp.	56.45%
D. Additional Results	50	≈ 6.49 pp.	10.47%
E. Experimental Details	56	≈ 6.43 pp.	10.37%

All detected figure and table locations

Main text

• Figure 1 · p. 3
• Table 1 · p. 8
• Table 2 · p. 8
• Figure 2 · p. 8
• Figure 3 · p. 9
• Figure 4 · p. 9
• Figure 5 · p. 9
• Figure 6 · p. 9

Attached appendix

• Table 3 · p. 12
• Table 4 · p. 12
• Table 5 · p. 12
• Table 6 · p. 59
• Figure 7 · p. 60
• Table 7 · p. 61
• Figure 8 · p. 62
• Figure 9 · p. 62

Argument and organization

1. 1 Introduction; 2 A Unified Model

   Defines a decision problem, positivity/MAR assumptions and observed-data-consistent ambiguity sets.

2. 3 Tractable Reformulations and Statistical Guarantees

   Separates discrete and continuous outcomes, with distinct reformulation and guarantee subsections.

3. 4 Numerical Experiments

   Tests scaling, radius effects, overall comparisons and controlled sensitivity in a contextual newsvendor problem.

Problem, claim and contribution

Missingness is tied to decision loss rather than reconstruction accuracy, and the introduction explains why imputing a dataset need not calibrate downstream decision uncertainty.

Sections 1–2, physical pp.1–3 · Main paper

Argument and section order

Reliability, statistical efficiency and tractability are announced as separate goals and then addressed by distinct propositions and numerical checks.

Section 2 continuation and Section 3, pp.4–7 · Main paper

Figures, captions and visual explanation

Separate runtime tables vary raw sample size versus latent-support size; separate cost/reliability panels expose the conservatism trade-off and sensitivity axes.

Tables 1–2 and Figure 2, p.8; Figures 3–6, p.9 · Main paper

Tables, comparisons and evidence

The experiments use 100 replications and distinguish 20–80% quantile bands from standard-deviation bands. Radius selection and test-information oracle diagnostics are explicitly separated in the appendix.

Section 4, pp.8–9; Appendix E.4–E.6, pp.58–59 · Main paper

Appendix and reproducibility

Baseline definitions, the candidate radius grid, deployable holdout selection and a diagnostic-only oracle are specified separately from mathematical proofs.

Appendices C–E; selected E.3–E.6, pp.58–59 · Main paper

Clarity and writing conventions

The main theory names complete-case positivity and MAR; it explains that unrestricted MNAR requires additional assumptions or external information.

Assumptions 2.4–2.5 and surrounding discussion, p.3 · Main paper

What to reuse—and what not to infer

Transferable lesson: Organize robust decision methods around assumptions, tractability and statistical guarantees, then evaluate decision quality and conservatism separately.

Boundary: The guarantees are conditional on positivity, MAR and further regularity; they do not cover unrestricted missing-not-at-random data. Empirical reliability compares realized cost with a validation estimate in Appendix E.5 and should not be equated automatically with theorem coverage. Figure 4’s caption says up to10,000 samples while its plotted labels and appendix table end at5,994.

Apply this lesson using the argument and evidence worksheet.

Inspection record and sources

Checked

2026-10-07

Reading status

Writing-focused manuscript scan + selected visuals inspected

Main text

Writing-focused scan across physical PDF pp.1–9, covering framing, section progression, definitions, method/evidence explanations, captions and scope. Physical pages extracted individually to avoid form-feed pagination errors. Selected full-page rasters inspected; not exhaustive line-by-line technical verification or experimental reproduction.

Appendix / supplement

Reference/impact boundary p.10 and appendix heading inventory A–E checked. Selected detailed reading of baselines, holdout/oracle tuning and reliability definitions E.3–E.6 (pp.58–59). Long proofs, continuous-covariate extensions and all experimental cases were not independently verified.

Visually inspected PDF pages

8, 9

This is a writing-focused scan of the manuscript and the stated supplementary scope: framing, organization, visual explanation, evidence presentation and wording. It is not a line-by-line proof audit, reproduction of results or exhaustive scientific review.

• Published proceedings PDF, PMLR volume 306, retrieved 2026-10-07 · 62 pages