{
  "schema_version": "1.0",
  "title": "Reproduction: Learning-Augmented Online Minimization with Dual Predictions",
  "emoji": "🔮",
  "space_id": "snaykey/repro-mr-autoencoder",
  "paper": {
    "arxiv_id": "2606.05380",
    "openreview_id": "JIbkbLYo3o"
  },
  "tags": [
    "icml2026-repro",
    "paper-JIbkbLYo3o"
  ],
  "updated_at": "2026-07-29T12:00:00+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: Learning-Augmented Online Minimization with Dual Predictions",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "children": []
      },
      {
        "slug": "claim-1-theorem-1-1-laminar",
        "title": "For laminar set cover, the proposed dual-prediction algorithm achieves E[ALG] = (1+epsilon)*OPT + O(R*eta/epsilon) for any constant epsilon>0, where eta measures dual prediction error (Theorem 1.1).",
        "children": []
      },
      {
        "slug": "claim-2-theorem-3-1-mts",
        "title": "For metrical task systems, the dual-prediction algorithm (Algorithm 3, an A*-style search minimizing d(s_{t-1},s)+c_t(s)+w_hat_t(s)) achieves a (1+eta/OPT)-competitive ratio driven by the span seminorm of Bellman-operator discrepancies (Theorem 3.1).",
        "children": []
      },
      {
        "slug": "claim-3-lemma-a-1-dual-stability",
        "title": "Optimal dual solutions are stable under instance perturbations, satisfying ||y1* - y2*||_1 = O(|X1 Delta X2|), whereas optimal primal solutions can change arbitrarily under a single-element perturbation (Lemma A.1).",
        "children": []
      },
      {
        "slug": "claim-4-lemma-a-3-caching",
        "title": "Event predictions for caching are similarly shown to be unstable, since a single prediction error can cause the competitive ratio to collapse (Lemma A.3).",
        "children": []
      },
      {
        "slug": "claim-5-experiments",
        "title": "On the parking permit problem, the learning-augmented dual-prediction algorithm achieves 1.8x to 4.4x better competitive ratios than classical algorithms at K=9 permit types, and it outperforms baselines on the k-server problem using real bike-sharing data (Experiments section).",
        "children": []
      },
      {
        "slug": "claim-6-lemma-a-4-general-setcover",
        "title": "For general (non-laminar) set cover, even perfect dual predictions cannot beat the classical H_m competitive ratio under the standard LP formulation, showing laminar structure is necessary for the improvement (Lemma A.4).",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "children": []
      }
    ]
  },
  "revision": 1
}