Writing study: A Causal Decomposition Approach for Fair Contextual Multi-Armed Bandits
← ICML 2026 oral writing corpus
Jiajun Chen, Jin Tian, Christopher John Quinn · 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
- 51 physical pages
- Before references / appendix
- ≈ 9.13 page-equivalents
- Main figures / tables
- 2 / 1
- Attached appendix figures / tables
- 2 / 1
- Attached appendix span
- ≈ 37.91 page-equivalents
Source-bound correction: Include the actual post-reference Contents page14 in the supporting-material envelope and join wrapped main headings.
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 | ≈ 1.89 pp. | 3.71% |
| 2. Problem Formulation | 3 | ≈ 1.72 pp. | 3.37% |
| 3. Non-parametric Contextual Bandits with Counterfactual Fairness Constraints | 4 | ≈ 1.91 pp. | 3.75% |
| 4. Logistic Bandits with Counterfactual Fairness Constraints | 6 | ≈ 2.33 pp. | 4.57% |
| 5. Numerical Experiments | 9 | ≈ 0.62 pp. | 1.22% |
| 6. Conclusion | 9 | ≈ 0.13 pp. | 0.25% |
| Acknowledgments | 9 | ≈ 0.15 pp. | 0.29% |
| Impact Statement | 10 | ≈ 0.09 pp. | 0.18% |
| References | 10 | ≈ 3.95 pp. | 7.75% |
| Contents | 14 | ≈ 0.96 pp. | 1.88% |
| A. Table of Notation | 15 | ≈ 1.04 pp. | 2.04% |
| B. Preliminaries | 16 | ≈ 1 pp. | 1.96% |
| C. Additional Related Works | 17 | ≈ 1 pp. | 1.96% |
| D. Proof for Section 2 | 18 | ≈ 3 pp. | 5.88% |
| E. Proof for Section 3 | 21 | ≈ 14.65 pp. | 28.73% |
| F. Proof for Section 4 | 35 | ≈ 12.67 pp. | 24.84% |
| G. Technical Lemmas | 48 | ≈ 2.04 pp. | 4% |
| H. Additional Discussions | 50 | ≈ 0.4 pp. | 0.78% |
| I. Experimental Details | 50 | ≈ 1.15 pp. | 2.25% |
All detected figure and table locations
Attached appendix
Argument and organization
- 1 Introduction; 2 Formulation
Defines mechanism-specific counterfactual fairness and its constrained online objective.
- 3 Non-parametric Bandits; 4 Logistic Bandits
Gives separate assumption, algorithm and guarantee blocks for two reward settings.
- 5 Numerical Experiments; 6 Conclusion
Illustrates the logistic setting and identifies exploration and MDP extensions as open directions.
Problem, claim and contribution
The introduction explains how aggregate disparity can cancel across pathways, motivating multiple fairness constraints rather than a single parity measure.
Introduction, p.1; Proposition 1 discussion, p.4 · Main paper
Argument and section order
Known context statistics, coverage and feasible-policy assumptions are stated before the algorithms; the logistic setting receives its own feature assumptions.
Section 3, p.5; Section 4, p.7 · Main paper
Figures, captions and visual explanation
The causal graph makes the assumed paths visible; the experiment figure separates penalized regret, cumulative reward and runtime into three panels.
Figure 1, p.4; Figure 2, p.9 · Main paper
Tables, comparisons and evidence
The empirical metric zeros reward for constraint-violating actions and the text acknowledges that unconstrained baselines optimize a different objective.
Numerical Experiments, p.9 · Main paper
Appendix and reproducibility
Additional discussion notes that even indirect effects can aggregate cancelling paths and explains that the non-parametric setting receives theory only.
Appendices H-I, p.50 · Main paper
Clarity and writing conventions
The formulation explicitly permits instantaneous violations while bounding cumulative violations, preventing the reader from interpreting the method as per-decision guaranteed fairness.
Section 2.2, p.4 · Main paper
What to reuse—and what not to infer
Transferable lesson: State the fairness notion, structural assumptions and violation timescale before presenting guarantees or comparing policies.
Boundary: Synthetic logistic experiments are not deployment validation; the specified causal model and known statistics are consequential assumptions, and mathematical fairness is not legal compliance.
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, 3, 4, 5, 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 50. Remaining appendix proofs and details were not exhaustively read. No separately linked supplement inspected.
- Visually inspected PDF pages
- 4, 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.