{
  "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"
}