logbook.json

{
  "schema_version": 1,
  "title": "Reproduction: Near-Optimal Regret for KL-Regularized Multi-Armed Bandits",
  "emoji": "🎰",
  "space_id": "snaykey/repro-kl-regularized-mab",
  "paper": {
    "openreview_id": "XarOZG8Un0"
  },
  "tags": [
    "icml2026-repro",
    "paper-XarOZG8Un0"
  ],
  "updated_at": "2026-07-25T12:00:00Z",
  "root": {
    "slug": "index",
    "title": "Reproduction: Near-Optimal Regret for KL-Regularized Multi-Armed Bandits",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "claim-1-high-reg-upper-bound",
        "title": "Theorem 4.2 establishes a high-probability regret upper bound of O~(ηK log^2 T) for KL-regularized multi-armed bandits in the high-regularization regime where η ≤ sqrt(T/K) (Section 4.2).",
        "file": "pages/claim-1-high-reg-upper-bound/page.md",
        "children": []
      },
      {
        "slug": "claim-2-low-reg-upper-bound",
        "title": "In the low-regularization regime (η ≥ sqrt(T/K)), the same analysis yields a regret bound of O~(sqrt(KT log T)), which is η-independent (Theorem 4.2, Section 4.2).",
        "file": "pages/claim-2-low-reg-upper-bound/page.md",
        "children": []
      },
      {
        "slug": "claim-3-high-reg-lower-bound",
        "title": "Theorem 5.3 provides a lower bound of Ω(ηK log(T/(η^2 K))) in the high-regularization regime, establishing near-tightness with the upper bound in Theorem 4.2 (Section 5, Theorem 5.3).",
        "file": "pages/claim-3-high-reg-lower-bound/page.md",
        "children": []
      },
      {
        "slug": "claim-4-low-reg-lower-bound",
        "title": "Theorem 5.1 gives a lower bound of Ω(sqrt(KT)) in the low-regularization regime via a two-point construction method (Section 6.1, Theorem 5.1).",
        "file": "pages/claim-4-low-reg-lower-bound/page.md",
        "children": []
      },
      {
        "slug": "claim-5-kl-ucb-algorithm",
        "title": "The KL-UCB algorithm uses an optimistic bonus term b_t(a) = sqrt(2 log(TK/delta) / (N_t(a) ∨ 1)) together with a novel peeling argument and Freedman's inequality to obtain tight high-probability bounds (Section 4.3).",
        "file": "pages/claim-5-kl-ucb-algorithm/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}