{
  "schema_version": "1.0",
  "title": "Reproduction: Multivariate Distributional Reinforcement Learning Using Sliced Divergences",
  "emoji": "🔪",
  "space_id": "snaykey/repro-cmdp-policy-opt",
  "paper": {
    "arxiv_id": "2605.31222",
    "openreview_id": "yeyUprQtAY"
  },
  "tags": [
    "icml2026-repro",
    "paper-yeyUprQtAY"
  ],
  "updated_at": "2026-07-29T00:00:00+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: Multivariate Distributional Reinforcement Learning Using Sliced Divergences",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "children": []
      },
      {
        "slug": "claim-1-theorem-1-metric",
        "title": "Theorem 1 proves that both uniform-sliced and max-sliced divergences retain the metric properties of the underlying base divergence when that base divergence is itself a metric on the reals (Section 4.1, Theorem 1).",
        "children": []
      },
      {
        "slug": "claim-2-theorem-2-uniform-contraction",
        "title": "Theorem 2 proves the distributional Bellman operator is a contraction in the sup-sliced divergence metric under uniform slicing with shared scalar discounting γI_d, with contraction factor c(γ) (Section 4.2, Theorem 2).",
        "children": []
      },
      {
        "slug": "claim-3-theorem-3-maxslice-matrix-contraction",
        "title": "Theorem 3 proves the max-slicing variant achieves a Bellman contraction under general dense per-state-action discount matrices Γ(s,a), resolving a previously open theoretical gap (Section 4.2, Theorem 3).",
        "children": []
      },
      {
        "slug": "claim-4-propositions-5-6-unbiased-gradient",
        "title": "Propositions 5 and 6 show uniform slicing preserves the unbiased-sample-gradient property needed for one-sample TD bootstrapping, while max-slicing and Wasserstein-based objectives violate this property (Section 4.4, Propositions 5-6).",
        "children": []
      },
      {
        "slug": "claim-5-section-3-3-complexity",
        "title": "SDRL supports sliced Wasserstein distance and sliced Cramér distance, each computable in O(Ln log n), as well as sliced Maximum Mean Discrepancy at O(Ln^2), as base divergences within the particle-based critic of Algorithm 1 (Section 3.3).",
        "children": []
      },
      {
        "slug": "claim-6-figure-2-chain-U",
        "title": "In the chain environment experiment, objectives satisfying the unbiased-gradient property (U) achieve a median Wasserstein distance of about 0.15-0.25 under standard TD updates, whereas objectives violating (U) degrade to roughly 0.4 or higher (Figure 2, Section 5).",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "children": []
      }
    ]
  },
  "revision": 1
}