logbook.json

{
  "schema_version": 1,
  "title": "Reproduction: Finite-time Convergence Analysis of Actor-Critic with Evolving Reward",
  "emoji": "🎯",
  "space_id": "snaykey/repro-actor-critic-evolving",
  "paper": {
    "openreview_id": "hocdjAEAIm"
  },
  "tags": [
    "icml2026-repro",
    "paper-hocdjAEAIm"
  ],
  "updated_at": "2026-08-02T00:00:00+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: Finite-time Convergence Analysis of Actor-Critic with Evolving Reward",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "claim-1-thm46-finite-time-bounds",
        "title": "Theorem 4.6 establishes finite-time bounds for single-timescale actor-critic with evolving rewards, with actor error G_T and critic error W_T each bounded by O(1/√T) + O(F_T·√T) + O(√(F_T/T)) + O(ε), where F_T measures cumulative reward-parameter variation over T iterations (Section 4.2).",
        "file": "pages/claim-1-thm46-finite-time-bounds/page.md",
        "children": []
      },
      {
        "slug": "claim-2-cor47-gradient-reward-rate",
        "title": "Corollary 4.7 shows that when the reward parameter is updated via gradient-based steps with step size η^φ_t = c_φ/t and bounded gradients, F_T = O(1/T), so the bounds reduce to G_T = O(1/√T) + O(ε) and W_T = O(1/√T) + O(ε), matching the best-known rate for static-reward actor-critic (Section 4.2).",
        "file": "pages/claim-2-cor47-gradient-reward-rate/page.md",
        "children": []
      },
      {
        "slug": "claim-3-prop48-distribution-mismatch",
        "title": "Proposition 4.8 bounds the distribution mismatch under Markovian sampling without dependence on the mixing time, improving prior convergence rates by a factor of log²T in the static-reward case (Section 4.3).",
        "file": "pages/claim-3-prop48-distribution-mismatch/page.md",
        "children": []
      },
      {
        "slug": "claim-4-assumption41-sufficient-exploration",
        "title": "Assumption 4.1 (sufficient exploration) requires the matrix A_θ to be negative definite with singular values bounded above by -λ, underpinning the actor-critic convergence analysis (Section 4, Assumption 4.1).",
        "file": "pages/claim-4-assumption41-sufficient-exploration/page.md",
        "children": []
      },
      {
        "slug": "claim-5-algorithm1-single-timescale",
        "title": "Algorithm 1 defines a single-timescale actor-critic scheme with step sizes η^θ_t = c_θ/√t and η^ω_t = c_ω/√t for policy and critic updates, alongside an arbitrary update rule for the evolving reward parameter φ_t (Section 3.3, Algorithm 1).",
        "file": "pages/claim-5-algorithm1-single-timescale/page.md",
        "children": []
      },
      {
        "slug": "executive-summary",
        "title": "executive-summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}