Writing study: Optimal Decision-Making Based on Prediction Sets
← ICML 2026 oral writing corpus
Tao Wang, Edgar Dobriban · Official ICML 2026 oral record
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
- 23 physical pages
- Before references / appendix
- ≈ 8.67 page-equivalents
- Main figures / tables
- 2 / 0
- Attached appendix figures / tables
- 1 / 0
- Attached appendix span
- ≈ 10.91 page-equivalents
Source-bound correction: Source-checked physical-page text restores wrapped top-level heading labels on pp. 3. Heading starts and measured positions are unchanged; this is label completeness, not a new section. Newly detected unnumbered impact/singular-acknowledgment statements are retained from the size-aware source extraction; authored heading corrections are unchanged.
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 | ≈ 1.77 pp. | 7.7% |
| 2. Optimal action selection from prediction sets | 3 | ≈ 2.05 pp. | 8.91% |
| 3. The Optimal Prediction Sets | 5 | ≈ 1.09 pp. | 4.74% |
| 4. Risk–optimal conformal prediction | 6 | ≈ 0.88 pp. | 3.83% |
| 5. Experiments | 7 | ≈ 2.16 pp. | 9.39% |
| 6. Discussion | 9 | ≈ 0.25 pp. | 1.09% |
| Acknowledgments | 9 | ≈ 0.08 pp. | 0.35% |
| Impact Statement | 9 | ≈ 0.05 pp. | 0.22% |
| References | 9 | ≈ 3.41 pp. | 14.83% |
| A. ROCP Workflow | 13 | ≈ 0.34 pp. | 1.48% |
| B. Additional Related Work and Background | 13 | ≈ 0.8 pp. | 3.48% |
| C. Proofs | 14 | ≈ 8.13 pp. | 35.35% |
| D. Experimental implementation details | 22 | ≈ 1.65 pp. | 7.17% |
All detected figure and table locations
Main text
Attached appendix
Argument and organization
- Problem and contribution
Uses the probability mass outside a prediction set to distinguish expected-loss robustness from purely in-set or quantile-risk reasoning.
- Argument sequence
Action selection is solved before prediction-set design, with conditional oracle coverage separated from the practical conformal procedure's marginal guarantee.
- Evidence and verification
The standard-loss case retains a higher realized loss than a comparator, while the severe-mismatch condition reveals the intended tail-risk advantage; uncertainty is over twenty random splits.
Problem, claim and contribution
Uses the probability mass outside a prediction set to distinguish expected-loss robustness from purely in-set or quantile-risk reasoning.
Introduction and related work, pp. 1-2 · Main paper
Argument and section order
Action selection is solved before prediction-set design, with conditional oracle coverage separated from the practical conformal procedure's marginal guarantee.
Sections 2-4, pp. 3-7; Appendix B, p. 14 · Main paper
Figures, captions and visual explanation
The theorem page defines edge cases beside the population optimization; repeated result panels compare two loss matrices using identical risk, realized-loss, coverage and critical-error axes.
Proposition 3.1/Remark 3.2, p. 5; Figure 1, p. 8; both PNGs inspected · Main paper
Tables, comparisons and evidence
The standard-loss case retains a higher realized loss than a comparator, while the severe-mismatch condition reveals the intended tail-risk advantage; uncertainty is over twenty random splits.
Section 5.1 and Figure 1, p. 8 · Main paper
Appendix and reproducibility
The driving-like test exposes region-derived labels, an independence-based probability construction and a hand-specified action loss instead of treating the setup as closed-loop driving.
Section 5.2, p. 8; Appendix D.1, pp. 22-23 · Main paper
Clarity and writing conventions
Plain-language interpretations of the out-of-set penalty accompany the formal result, and the toy application disclaimer is explicit in the main text.
Introduction, p. 2; Section 5.2, p. 8 · Main paper
What to reuse—and what not to infer
Transferable lesson: Derive decisions before optimizing uncertainty sets, and test loss regimes where the proposed distinction should matter as well as where it should not.
Boundary: Finite-sample marginal coverage under exchangeability is not conditional coverage or a clinical/driving safety certificate; empirical benefits depend on the chosen loss specification.
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 distributed manuscript scan, not exhaustive technical/proof validation. Sections 1-6, pp. 1-9: out-of-set loss motivation, minimax action rule, population set design, conformalized estimator and two decision experiments.
- Appendix / supplement
- Writing-focused appendix scan; code, data and external assets not executed. Appendices A-D, pp. 13-23: workflow, extended related work, measurability/duality proofs and exact toy-driving label, probability and loss construction.
- Visually inspected PDF pages
- 5, 8
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.