repro-bundle-v0/PROMPT.md

Fetching papers index and claims data...

Found Paper #13517: Title: Steady-State Behavior of Constant-Stepsize Stochastic Approximation: Gaussian Approximation and Tail Bounds OpenReview ID: m4TAzup6Yc arXiv ID: 2602.13960 OpenReview URL: https://openreview.net/forum?id=m4TAzup6Yc

Major Claims to Verify (the criteria for the Logbook Judge):

• Claim 1: Theorem 3.1 (i.i.d. noise) and Theorem 4.1 (Markovian noise) bound the Wasserstein distance between the centered-scaled steady state Y^(α) = (X^(α) − x*)/√α and its Gaussian limit N(0, Σ_Y) by U√α log(1/α) (Theorems 3.1 and 4.1).
• Claim 2: Proposition 3.1 establishes an explicit non-asymptotic Wasserstein bound of order O(α^{1/2} log(1/α)) for constant-stepsize SGD on smooth, strongly convex objectives (Proposition 3.1).
• Claim 3: Propositions 3.2 and 3.3 extend the same O(α^{1/2} log(1/α)) Wasserstein bound to linear stochastic approximation with a Hurwitz matrix and to contractive nonlinear stochastic approximation, respectively (Propositions 3.2 and 3.3, Section 3.2.2, Section 3.2.3).
• Claim 4: For one-dimensional projections, the paper derives a non-uniform Berry-Esseen-type tail bound |P(⟨Y^(α),ζ⟩ > a) − P(Z_ζ > a)| ≤ C_d α^{1/4} log^{1/2}(1/α) / a, which improves as the deviation level a grows (Section 4).
• Claim 5: Proposition 4.1 extends the Gaussian approximation and tail bounds for SGD, linear SA, and contractive nonlinear SA from i.i.d. noise to Markovian noise (Proposition 4.1, Section 4).
• Claim 6: Proposition 5.1 shows a different convergence rate of order α^{1/h} for constant-stepsize SA applied to general convex objectives with Gibbs-type limiting distributions (Proposition 5.1, Section 5).

============================== GENERATED AGENT PROMPT ==============================

First, read the challenge instructions:

curl -sL https://huggingface.co/datasets/ICML-2026-agent-repro/challenge/resolve/main/README.md

Your job is to reproduce the ICML 2026 paper #13517 — Steady-State Behavior of Constant-Stepsize Stochastic Approximation: Gaussian Approximation and Tail Bounds (OpenReview id: m4TAzup6Yc). Here are the major claims that you should verify:

• Claim 1: Theorem 3.1 (i.i.d. noise) and Theorem 4.1 (Markovian noise) bound the Wasserstein distance between the centered-scaled steady state Y^(α) = (X^(α) − x*)/√α and its Gaussian limit N(0, Σ_Y) by U√α log(1/α) (Theorems 3.1 and 4.1).
• Claim 2: Proposition 3.1 establishes an explicit non-asymptotic Wasserstein bound of order O(α^{1/2} log(1/α)) for constant-stepsize SGD on smooth, strongly convex objectives (Proposition 3.1).
• Claim 3: Propositions 3.2 and 3.3 extend the same O(α^{1/2} log(1/α)) Wasserstein bound to linear stochastic approximation with a Hurwitz matrix and to contractive nonlinear stochastic approximation, respectively (Propositions 3.2 and 3.3, Section 3.2.2, Section 3.2.3).
• Claim 4: For one-dimensional projections, the paper derives a non-uniform Berry-Esseen-type tail bound |P(⟨Y^(α),ζ⟩ > a) − P(Z_ζ > a)| ≤ C_d α^{1/4} log^{1/2}(1/α) / a, which improves as the deviation level a grows (Section 4).
• Claim 5: Proposition 4.1 extends the Gaussian approximation and tail bounds for SGD, linear SA, and contractive nonlinear SA from i.i.d. noise to Markovian noise (Proposition 4.1, Section 4).
• Claim 6: Proposition 5.1 shows a different convergence rate of order α^{1/h} for constant-stepsize SA applied to general convex objectives with Gibbs-type limiting distributions (Proposition 5.1, Section 5).

Step 1 — scaffold the canonical logbook (mandatory):

python3 repro/scaffold_icml_logbook.py --title 'Reproduction: Steady-State Behavior of Constant-Stepsize Stochastic Approximation: Gaussian Approximation and Tail Bounds' --orid m4TAzup6Yc --openreview-url 'https://openreview.net/forum?id=m4TAzup6Yc' --arxiv 2602.13960 --claims-json '["Theorem 3.1 (i.i.d. noise) and Theorem 4.1 (Markovian noise) bound the Wasserstein distance between the centered-scaled steady state Y^(\u03b1) = (X^(\u03b1) \u2212 x*)/\u221a\u03b1 and its Gaussian limit N(0, \u03a3_Y) by U\u221a\u03b1 log(1/\u03b1) (Theorems 3.1 and 4.1).", "Proposition 3.1 establishes an explicit non-asymptotic Wasserstein bound of order O(\u03b1^{1/2} log(1/\u03b1)) for constant-stepsize SGD on smooth, strongly convex objectives (Proposition 3.1).", "Propositions 3.2 and 3.3 extend the same O(\u03b1^{1/2} log(1/\u03b1)) Wasserstein bound to linear stochastic approximation with a Hurwitz matrix and to contractive nonlinear stochastic approximation, respectively (Propositions 3.2 and 3.3, Section 3.2.2, Section 3.2.3).", "For one-dimensional projections, the paper derives a non-uniform Berry-Esseen-type tail bound |P(\u27e8Y^(\u03b1),\u03b6\u27e9 > a) \u2212 P(Z_\u03b6 > a)| \u2264 C_d \u03b1^{1/4} log^{1/2}(1/\u03b1) / a, which improves as the deviation level a grows (Section 4).", "Proposition 4.1 extends the Gaussian approximation and tail bounds for SGD, linear SA, and contractive nonlinear SA from i.i.d. noise to Markovian noise (Proposition 4.1, Section 4).", "Proposition 5.1 shows a different convergence rate of order \u03b1^{1/h} for constant-stepsize SA applied to general convex objectives with Gibbs-type limiting distributions (Proposition 5.1, Section 5)."]'

Use Space title Reproduction: Steady-State Behavior of Constant-Stepsize Stochastic Approximation: Gaussian Approximation and Tail Bounds and publish slug repro-steady-state-behavior-of-constant-stepsize-stochastic-approximation-gaussian-approximation (never the OpenReview id).

Logbook structure (fixed order):

• Index: title + paper link + Pages table only
• Executive summary: pinned summary + Scope & cost table + pinned Chenruishuo/posterly poster (poster_embed.html)
• Claim 1 … Claim N: one page per claim
• Conclusion: reproduction bundle artifact + download/rerun instructions

Try to verify the claims as much as you can locally or using Hugging Face Jobs. Link every Hub model, dataset, Job, Bucket, and GitHub repo in logbook cells.

Last step — validate, then publish:

curl -sL https://huggingface.co/spaces/ICML-2026-agent-repro/challenge/raw/main/scripts/validate_icml_logbook.py | python3 - --space /repro-steady-state-behavior-of-constant-stepsize-stochastic-approximation-gaussian-approximation && trackio logbook publish /repro-steady-state-behavior-of-constant-stepsize-stochastic-approximation-gaussian-approximation

====================================================================================

Running scaffolding command: 'C:\tools\Python\Python313\python.exe' 'C:\Users\Muhammad Mesum Raza\Desktop\wsl-data\ConstantStepsizeSA\repro\scaffold_icml_logbook.py' --title 'Reproduction: Steady-State Behavior of Constant-Stepsize Stochastic Approximation: Gaussian Approximation and Tail Bounds' --orid m4TAzup6Yc --openreview-url 'https://openreview.net/forum?id=m4TAzup6Yc' --arxiv 2602.13960 --claims-json '["Theorem 3.1 (i.i.d. noise) and Theorem 4.1 (Markovian noise) bound the Wasserstein distance between the centered-scaled steady state Y^(\u03b1) = (X^(\u03b1) \u2212 x*)/\u221a\u03b1 and its Gaussian limit N(0, \u03a3_Y) by U\u221a\u03b1 log(1/\u03b1) (Theorems 3.1 and 4.1).", "Proposition 3.1 establishes an explicit non-asymptotic Wasserstein bound of order O(\u03b1^{1/2} log(1/\u03b1)) for constant-stepsize SGD on smooth, strongly convex objectives (Proposition 3.1).", "Propositions 3.2 and 3.3 extend the same O(\u03b1^{1/2} log(1/\u03b1)) Wasserstein bound to linear stochastic approximation with a Hurwitz matrix and to contractive nonlinear stochastic approximation, respectively (Propositions 3.2 and 3.3, Section 3.2.2, Section 3.2.3).", "For one-dimensional projections, the paper derives a non-uniform Berry-Esseen-type tail bound |P(\u27e8Y^(\u03b1),\u03b6\u27e9 > a) \u2212 P(Z_\u03b6 > a)| \u2264 C_d \u03b1^{1/4} log^{1/2}(1/\u03b1) / a, which improves as the deviation level a grows (Section 4).", "Proposition 4.1 extends the Gaussian approximation and tail bounds for SGD, linear SA, and contractive nonlinear SA from i.i.d. noise to Markovian noise (Proposition 4.1, Section 4).", "Proposition 5.1 shows a different convergence rate of order \u03b1^{1/h} for constant-stepsize SA applied to general convex objectives with Gibbs-type limiting distributions (Proposition 5.1, Section 5)."]'Scaffolded logbook: Reproduction: Steady-State Behavior of Constant-Stepsize Stochastic Approximation: Gaussian Approximation and Tail Bounds Publish slug: repro-steady-state-behavior-of-constant-stepsize-stochastic-approximation-gaussian-approximation Publish target: /repro-steady-state-behavior-of-constant-stepsize-stochastic-approximation-gaussian-approximation

Next steps:

1. Reproduce each claim (log commands, Hub assets, results)
2. Fill Executive summary + poster_embed.html (Chenruishuo/posterly)
3. Add reproduction bundle artifact on Conclusion
4. curl -sL …/validate_icml_logbook.py | python3 - --space /repro-steady-state-behavior-of-constant-stepsize-stochastic-approximation-gaussian-approximation
5. trackio logbook publish /repro-steady-state-behavior-of-constant-stepsize-stochastic-approximation-gaussian-approximation

Logbook successfully scaffolded!