| { |
| "schema_version": 1, |
| "title": "Reproduction: Asymptotically Optimal Sequential Testing with Markovian Data", |
| "emoji": "🎯", |
| "space_id": "ProCreations/repro-asymptotically-optimal-sequential-testing-with-markovian-data", |
| "paper": { |
| "arxiv_id": "2602.17587" |
| }, |
| "tags": [ |
| "icml2026-repro", |
| "paper-YEckWPoS09" |
| ], |
| "claims": [ |
| "Theorem 3.3 gives a non-asymptotic instance-dependent lower bound on the expected stopping time, E_Q[tau_alpha] ≥ (log(1/alpha)/D_M^inf(Q,P) − 2C_Q/min_i pi_i)^+, where D_M^inf(Q,P) is a stationary-weighted projection distance and C_Q bounds a Poisson-equation solution (Theorem 3.3).", |
| "Proposition 3.1 bounds the Poisson-equation solution constant C_Q via the pseudo-spectral gap of the underlying Markov chain (Section 3, Proposition 3.1).", |
| "The proposed Sequential Markov Chain Test (Algorithm 1) builds an empirical transition kernel and a martingale statistic L_t accumulating row-wise KL divergences from the null class, stopping when L_t exceeds an adaptive boundary beta_t (Section 4, Algorithm 1).", |
| "Theorem 4.1 proves the proposed test is alpha-correct and asymptotically optimal, with limsup_{alpha->0} E_Q[tau_alpha]/log(1/alpha) ≤ 1/D_M^inf(Q,P), matching the Theorem 3.3 lower bound (Theorem 4.1).", |
| "Theorem 4.4 extends the one-sided asymptotic optimality result to the two-sided testing setting (Section 4.2, Theorem 4.4).", |
| "The framework is applied to detect MCMC transition-kernel misspecification (Section 5.1, Corollary 5.1) and to validate linear transition dynamics in MDPs (Section 5.2, Corollary 5.3)." |
| ], |
| "updated_at": "2026-07-26T15:52:00+00:00", |
| "root": { |
| "slug": "index", |
| "title": "Reproduction: Asymptotically Optimal Sequential Testing with Markovian Data", |
| "file": "pages/index.md", |
| "children": [ |
| { |
| "slug": "executive-summary", |
| "title": "Executive summary", |
| "file": "pages/executive-summary/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-0-judge-first-scorecard", |
| "title": "Claim 0: Judge-first scorecard — six direct verdicts", |
| "file": "pages/claim-0-judge-first-scorecard/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-1-theorem-3-3-lower-bound", |
| "title": "Claim 1: Theorem 3.3 gives a non-asymptotic instance-dependent lower bound on the expected stopping time, E_Q[tau_alpha] ≥ (log(1/alpha)/D_M^inf(Q,P) − 2C_Q/min_i pi_i)^+, where D_M^inf(Q,P) is a stationary-weighted projection distance and C_Q bounds a Poisson-equation solution (Theorem 3.3).", |
| "file": "pages/claim-1-theorem-3-3-lower-bound/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-2-proposition-3-1-poisson-bound", |
| "title": "Claim 2: Proposition 3.1 bounds the Poisson-equation solution constant C_Q via the pseudo-spectral gap of the underlying Markov chain (Section 3, Proposition 3.1).", |
| "file": "pages/claim-2-proposition-3-1-poisson-bound/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-3-algorithm-1-sequential-test", |
| "title": "Claim 3: The proposed Sequential Markov Chain Test (Algorithm 1) builds an empirical transition kernel and a martingale statistic L_t accumulating row-wise KL divergences from the null class, stopping when L_t exceeds an adaptive boundary beta_t (Section 4, Algorithm 1).", |
| "file": "pages/claim-3-algorithm-1-sequential-test/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-4-theorem-4-1-correctness-and-optimality", |
| "title": "Claim 4: Theorem 4.1 proves the proposed test is alpha-correct and asymptotically optimal, with limsup_{alpha->0} E_Q[tau_alpha]/log(1/alpha) ≤ 1/D_M^inf(Q,P), matching the Theorem 3.3 lower bound (Theorem 4.1).", |
| "file": "pages/claim-4-theorem-4-1-correctness-and-optimality/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-5-theorem-4-4-two-sided-test", |
| "title": "Claim 5: Theorem 4.4 extends the one-sided asymptotic optimality result to the two-sided testing setting (Section 4.2, Theorem 4.4).", |
| "file": "pages/claim-5-theorem-4-4-two-sided-test/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-6-mcmc-and-linear-mdp-applications", |
| "title": "Claim 6: The framework is applied to detect MCMC transition-kernel misspecification (Section 5.1, Corollary 5.1) and to validate linear transition dynamics in MDPs (Section 5.2, Corollary 5.3).", |
| "file": "pages/claim-6-mcmc-and-linear-mdp-applications/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "conclusion", |
| "title": "Conclusion", |
| "file": "pages/conclusion/page.md", |
| "children": [] |
| } |
| ] |
| }, |
| "agent_view_tokens": 9000, |
| "revision": "1785081120000000000" |
| } |
|
|
