Writing study: What Preferences Can—and Cannot—Predict in Multi-Agent Online Learning
← ICML 2026 oral writing corpus
Omar Abbadi, Rida Laraki, Panayotis Mertikopoulos · 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
- 47 physical pages
- Before references / appendix
- ≈ 9.23 page-equivalents
- Main figures / tables
- 5 / 0
- Attached appendix figures / tables
- 10 / 0
- Attached appendix span
- ≈ 34.91 page-equivalents
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 | ≈ 2 pp. | 4.26% |
| 2 Preliminaries | 3 | ≈ 0.52 pp. | 1.11% |
| 3 Preferences, learning and stability | 3 | ≈ 2.26 pp. | 4.81% |
| 4 Implications of dynamic stability | 6 | ≈ 0.63 pp. | 1.34% |
| 5 Implications of preferential stability | 6 | ≈ 1.18 pp. | 2.51% |
| 6 Recovering dynamic stability | 7 | ≈ 1.86 pp. | 3.96% |
| 7 Concluding remarks | 9 | ≈ 0.25 pp. | 0.53% |
| Acknowledgments | 10 | ≈ 0.13 pp. | 0.28% |
| Impact statement | 10 | ≈ 0.05 pp. | 0.11% |
| References | 10 | ≈ 2.86 pp. | 6.09% |
| A Further related work | 13 | ≈ 0.49 pp. | 1.04% |
| B Preference graphs | 13 | ≈ 3.29 pp. | 7% |
| C Attractors and chain transitivity | 16 | ≈ 1.22 pp. | 2.6% |
| D Regularizers and choice maps | 18 | ≈ 3 pp. | 6.38% |
| E Strategy dynamics | 21 | ≈ 2.49 pp. | 5.3% |
| F Omitted proofs from Section 4 | 23 | ≈ 3.85 pp. | 8.19% |
| G Omitted proofs from Section 5 | 27 | ≈ 11 pp. | 23.4% |
| H Omitted proofs from Section 6 | 38 | ≈ 9.59 pp. | 20.4% |
All detected figure and table locations
Argument and organization
- 1 Introduction; 2 Preliminaries; 3 Preferences, learning and stability
Defines the distinction between ordinal information and continuous learning dynamics.
- 4 Implications of dynamic stability; 5 Implications of preferential stability
Tests both directions of the proposed correspondence and isolates the subgame exception.
- 6 Recovering dynamic stability; 7 Concluding remarks
Adds a payoff-dependent sufficient condition while preserving unresolved converse questions.
Problem, claim and contribution
A question about stable sets replaces a universal convergence-to-equilibrium premise, allowing recurrence and chaotic behavior to remain part of the problem.
Introduction, p.1 · Main paper
Argument and section order
The two implication directions organize the theorem sequence, followed by an explicit counterexample and a stronger sufficient condition.
Sections 4-6, pp.6-8 · Main paper
Figures, captions and visual explanation
Paired cube graphs and trajectories show when ordinal closure matches or fails to match dynamics; four concluding trajectories retain the same preference graph while changing one payoff.
Figure 1, p.2; Figure 5, p.9 · Main paper
Tables, comparisons and evidence
The theorem statements distinguish FTRL from its induced strategy flow and distinguish subgames from arbitrary spans, rather than treating every stability concept as interchangeable.
Sections 3-6, pp.5-8 · Main paper
Appendix and reproducibility
The appendices supply related-work qualifications, regularizer assumptions and staged proofs; the main text points to them for the score-space argument and energy constructions.
Appendices A, D and F, pp.13,18,24 · Main paper
Clarity and writing conventions
A footnote acknowledges a correction: the counterexample refutes a stronger pure-local-source variant, not the original conjecture involving a mixed local source.
Related-work discussion and footnote 1, p.3 · Main paper
What to reuse—and what not to infer
Transferable lesson: Organize a theoretical paper around directions of implication and boundary cases, and keep the precise conjecture resolved distinct from nearby claims left open.
Boundary: Radness is sufficient rather than necessary in general; polynomial tests are measured in the explicit payoff-table size, not a succinct large multi-agent representation.
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-oriented scan of the main argument through physical p.9, with focused physical-page text inspection on 1, 2, 3, 5, 6, 7, 8, 9. Framing, section progression, mechanism/proof explanation, displays, comparison conditions and conclusions were inspected. This is not exhaustive technical reading, proof verification or reproduction.
- Appendix / supplement
- Appendix organization and main-text pointers were checked; focused text inspection of physical pages 13, 18, 24. Remaining appendix proofs and details were not exhaustively read. No separately linked supplement inspected.
- Visually inspected PDF pages
- 2, 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.