Writing study: Learning Human-Robot Collaboration via Heterogeneous-Agent Lyapunov Policy Optimization

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← ICML 2026 oral writing corpus

Hao Zhang, Yaru Niu, Yikai Wang, Ding Zhao, Eric H. Tseng · 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: Training, objectives & optimization (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

15 physical pages

Before references / appendix

≈ 8.54 page-equivalents

Main figures / tables

8 / 3

Attached appendix figures / tables

0 / 6

Attached appendix span

≈ 3.91 page-equivalents

Before references / appendix: ≈ 56.93%References / intervening material: ≈ 17%Attached appendix: ≈ 26.07%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 pp.	6.67%
2. Related Work	2	≈ 0.51 pp.	3.4%
3. Preliminaries	2	≈ 0.51 pp.	3.4%
4. Methodology: The HALO Framework	3	≈ 1.47 pp.	9.8%
5. Theoretical Analysis	4	≈ 0.57 pp.	3.8%
6. Experiments and Results	5	≈ 3.41 pp.	22.73%
7. Conclusion	8	≈ 0.32 pp.	2.13%
Acknowledgements	9	≈ 0.08 pp.	0.53%
Impact Statement	9	≈ 0.32 pp.	2.13%
References	9	≈ 2.54 pp.	16.93%
A. Detailed theoretical derivations	12	≈ 1.54 pp.	10.27%
B. Implementation and experimentation details	13	≈ 2.37 pp.	15.8%

All detected figure and table locations

Main text

• Figure 1 · p. 3
• Figure 2 · p. 5
• Figure 3 · p. 5
• Table 1 · p. 6
• Figure 4 · p. 6
• Figure 5 · p. 6
• Figure 6 · p. 7
• Figure 7 · p. 7
• Table 2 · p. 7
• Figure 8 · p. 8
• Table 3 · p. 8

Attached appendix

• Table 4 · p. 14
• Table 5 · p. 14
• Table 6 · p. 14
• Table 7 · p. 15
• Table 8 · p. 15
• Table 9 · p. 15

Argument and organization

1. Problem and contribution

   Locates the proposed stability certificate in policy-parameter space and defines coordination disagreement as the difference between independent and team gradient fields.

2. Argument sequence

   A constrained projection and HVP implementation precede theorem conditions, then task performance, mechanism diagnostics and real-world transfer are separated.

3. Evidence and verification

   The descent statement requires a state-dependent step-size bound and smoothness; the physical SLH table retains a 20% drop rate rather than supporting an absolute safety claim.

Problem, claim and contribution

Locates the proposed stability certificate in policy-parameter space and defines coordination disagreement as the difference between independent and team gradient fields.

Sections 1 and 4, pp. 2-3 · Main paper

Argument and section order

A constrained projection and HVP implementation precede theorem conditions, then task performance, mechanism diagnostics and real-world transfer are separated.

Sections 4-6, pp. 3-8 · Main paper

Figures, captions and visual explanation

Simulation infrastructure and reward dynamics share one figure, while physical demonstrations mark temporal progression and accompany a five-trial table retaining nonzero drop rates.

Figure 2, p. 5; Figure 8 and Table 3, p. 8; both PNGs inspected · Main paper

Tables, comparisons and evidence

The descent statement requires a state-dependent step-size bound and smoothness; the physical SLH table retains a 20% drop rate rather than supporting an absolute safety claim.

Assumption 5.1/Theorem 5.2, pp. 4-5; Table 3, p. 8 · Main paper

Appendix and reproducibility

Baseline documentation gives the same network size and training steps but explicitly different partner representations and collaborative features, making the comparison's residual confounds visible.

Appendix B.4 and Tables 7-9, p. 15 · Main paper

Clarity and writing conventions

Short proof summaries explain the role of the Lyapunov potential, but strongly worded coordination/stability claims must retain the parameter-space and small physical-study boundaries.

Section 5, pp. 4-5; Section 6.5, pp. 7-8 · Main paper

What to reuse—and what not to infer

Transferable lesson: Keep the formal certificate's space and assumptions separate from behavioral outcomes, and report failures alongside physical demonstrations.

Boundary: Gradient-gap convergence is not physical safety or global reward optimality; five trials, motion-capture dependence and changed partner features limit deployment generalization.

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 1-7, pp. 1-8: coordination-gradient mismatch, projected update, HVP implementation, conditional convergence analysis, simulation diagnostics and physical collaboration tests.

Appendix / supplement

Writing-focused appendix scan; code, data and external assets not executed. Appendices A-B, pp. 12-15: gradient/projection and convergence derivations, hierarchical controller, hyperparameters and scripted-partner baseline implementation.

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.

• Published ICML 2026 proceedings PDF, PMLR volume 306; retrieved 2026-10-07. Public OpenReview decision notes were not independently reverified. · 15 pages