{
  "schema_version": 1,
  "title": "Optimal Design for Multinomial Logit Model with Applications to Best Assortment Identification",
  "emoji": "📐",
  "space_id": "snaykey/repro-multinomial-logit-design",
  "paper": {
    "arxiv_id": "2605.25592",
    "openreview_id": "FhBOdaIcUw"
  },
  "tags": [
    "icml2026-repro",
    "paper-FhBOdaIcUw"
  ],
  "updated_at": "2026-07-28T00:00:00+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: Optimal Design for Multinomial Logit Model with Applications to Best Assortment Identification",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "children": []
      },
      {
        "slug": "claim-1-theorem-3-3-milp-lmo",
        "title": "Theorem 3.3 gives a mixed-integer linear programming (MILP) reformulation of the linear maximization oracle (LMO) needed for optimal design in the multinomial logit (MNL) model (Theorem 3.3).",
        "children": []
      },
      {
        "slug": "claim-2-theorem-3-5-lifted-frank-wolfe",
        "title": "Theorem 3.5 establishes a stopping/approximation guarantee for a lifted Frank-Wolfe algorithm that solves the MNL optimal design problem without requiring exact LMO calls (Theorem 3.5).",
        "children": []
      },
      {
        "slug": "claim-3-theorem-4-4-sample-complexity",
        "title": "Theorem 4.4 shows the proposed best assortment identification algorithm achieves sample complexity O~(d log(N/δ)(1/Δmin² + 1/(κΔmin)) + T0), where d is the feature dimension, N is the number of arms/assortments, and Δmin is the minimum reward gap (Theorem 4.4).",
        "children": []
      },
      {
        "slug": "claim-4-corollary-4-5-lifted-design",
        "title": "Corollary 4.5 shows that using the lifted G-optimal design in place of the MILP-based design multiplies the sample complexity by a factor of only (1+ε_lift), while remaining computationally tractable (Corollary 4.5).",
        "children": []
      },
      {
        "slug": "claim-5-table-1-lmo-runtime",
        "title": "Table 1 reports average LMO runtime comparisons across methods (MILP vs. lifted surrogate) for varying problem sizes (Table 1).",
        "children": []
      },
      {
        "slug": "claim-6-figure-1-stopping-time",
        "title": "Figure 1 reports the average stopping time τ of the best assortment identification algorithm as N (number of arms) is varied over {30, 50, 100, 200} and K (assortment size) over {3, 4, 5}, using feature dimension d=5 and failure probability δ=0.05 (Figure 1).",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "children": []
      }
    ]
  },
  "agent_view_tokens": 0,
  "revision": 1
}