Writing study: Non-Asymptotic Analysis of (Sticky) Track-and-Stop

← ICLR 2026 oral writing corpus

Riccardo Poiani, Martino Bernasconi, Andrea Celli · Official ICLR 2026 oral record

Figure, table and section ledger

Editorial contribution type: Theory & formal foundations (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: 31 physical pages
Before references / appendix: ≈ 10.34 page-equivalents
Main figures / tables: 0 / 0
Attached appendix figures / tables: 0 / 0
Attached appendix span: ≈ 18.89 page-equivalents

Before references / appendix: ≈ 33.35%References / intervening material: ≈ 5.71%Attached appendix: ≈ 60.94%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Source-bound correction: Independent PDF text and boundary audit: appendix navigation/overview begins before first lettered substantive heading. Physical heading coordinates taken from source-pinned Poppler bbox.

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	≈ 1.75 pp.	5.65%
2 BACKGROUND	3	≈ 2.18 pp.	7.03%
3 NON-ASYMPTOTIC ANALYSIS FOR TRACK-AND-STOP	5	≈ 2.33 pp.	7.52%
4 NON-ASYMPTOTIC ANALYSIS FOR STICKY TRACK-AND-STOP	7	≈ 2.55 pp.	8.23%
5 CONCLUSION	10	≈ 0.78 pp.	2.52%
ACKNOWLEDGMENTS	11	≈ 0.13 pp.	0.42%
REPRODUCIBILITY STATEMENT	11	≈ 0.1 pp.	0.32%
REFERENCES	11	≈ 1.77 pp.	5.71%
CONTENTS	13	≈ 1 pp.	3.23%
A STRUCTURED BANDITS	14	≈ 0.29 pp.	0.94%
B LOWER BOUND	14	≈ 0.95 pp.	3.06%
C ON THE ASSUMPTIONS	15	≈ 0.88 pp.	2.84%
D NON-ASYMPTOTIC BOUND FOR TRACK-AND-STOP	16	≈ 4.02 pp.	12.97%
E A SIMPLE FIX WITHOUT USING PROJECTIONS	20	≈ 0.61 pp.	1.97%
F NON-ASYMPTOTIC BOUND FOR STICKY TRACK-AND-STOP	20	≈ 5.9 pp.	19.03%
G AN EXPLICIT BOUND	26	≈ 2.77 pp.	8.94%
H AUXILIARY TOOLS	29	≈ 2.47 pp.	7.97%

All detected figure and table locations

Main text

No recognized caption labels.

Attached appendix

No recognized caption labels.

Argument and organization

Background
Defines single versus multiple answers, oracle weights, sampling and stopping.
Non-asymptotic analyses
Presents two parallel theorem–interpretation–proof-sketch narratives.
Explicit bounds and auxiliary tools
Turns implicit stopping conditions into rates and isolates reusable lemmas.

Problem, claim and contribution

The gap is carefully about finite-confidence analysis of established algorithms, not introducing a new bandit solver. Related work distinguishes modifying the algorithm to stabilize sampling from analyzing its original behavior.

§1–1.1, pp.1–3 · Main paper

Argument and section order

Background defines correct answers, optimal answers and oracle-weight sets separately. This prepares the exact obstruction in multiple-answer problems: a convex combination of optimal allocations need not remain optimal.

§2, pp.3–5 · Main paper

Figures, captions and visual explanation

There are no empirical plots. Theorem 2's displayed bound, explanatory paragraphs and named proof sketch form the page's visual hierarchy; the problem-dependent delay is interpreted immediately instead of leaving constants unexplained.

Theorem 2 and following discussion, p.8 · Main paper

Tables, comparisons and evidence

The main proof explains how the stopping statistic is related to accumulated sampling information, with sublinear errors. It explicitly identifies the step using uniqueness, preventing the single-answer argument from silently claiming the multiple-answer result.

Theorem 1 proof sketch and proof idea, pp.6–7 · Main paper

Appendix and reproducibility

Complete proofs are separated from assumptions, projection removal, explicit rates and auxiliary concentration tools. The reproducibility statement points to these mathematical artifacts rather than implying that a theoretical paper must supply experiments.

Reproducibility statement, p.11; appendices C–H, pp.15–31 · Main paper

Clarity and writing conventions

The conclusion names unresolved finite-confidence gaps and infinite-answer extensions. However, practical usefulness should remain distinct from demonstrated empirical tightness: there are no new experiments and the explicit constants can be large.

§5, p.10; Appendix G, pp.26–29 · Main paper

What to reuse—and what not to infer

Transferable lesson: For theory papers, pair each result with its assumptions, interpretation and one decisive proof idea; explain precisely why a familiar argument fails in the harder setting.

Boundary: The main analysis projects estimated means; unprojected guarantees require additional reasoning. Appendix E's assertion that F is positive needs means strictly inside the chosen bounding interval, not merely a closed interval inside an open parameter domain. Appendix H's displayed threshold is Gaussian-specific; general families use a different threshold. This writing study is not a proof certification.

Apply this lesson using the argument and evidence worksheet.

Inspection record and sources

Checked: 2026-09-19
Reading status: Full text + selected visuals inspected
Main text: pp.1–10, §§1–5; reproducibility and references pp.11–12
Appendix / supplement: pp.13–31, contents and appendices A–H, including complete proofs and stopping threshold
Visually inspected PDF pages: 8, 27

official ICLR 2026 proceedings PDF · 31 pages