{
  "abstract": "In multi-objective reinforcement learning, preferences may be specified only after data collection, requiring one dataset to support a continuum of reward trade-offs. We study finite discounted Markov decision processes with unknown transitions, $S$ states, $A$ actions, and $m$ known reward functions taking values in $[0,1]$, given access to a generative model. The learner must provide an $\\varepsilon$-optimal policy for every convex combination of these rewards without further sampling, with a guarantee that holds simultaneously over all preferences and initial states. Writing $H=(1-γ)^{-1}$, we establish the constant-confidence minimax sample complexity $\\widetildeΘ\\!\\left( \\frac{SAH^3}{\\varepsilon^2}\\min\\{S,\\log(em)\\} \\right)$, where the suppressed factors are logarithmic in $S,A,H,\\varepsilon^{-1}$ and the dependence on $m$ is explicit. Thus, up to these logarithmic factors, the worst-case statistical cost of supporting all preferences grows logarithmically with the number of objectives and saturates at the number of states. The upper bound uses uniform state--action sampling and empirical planning, with reward rounding in the logarithmic-objective regime. Its analysis chains optimal-value increments over covers of the reward hull. A one-sided Bellman variance bound controls signed value differences under a second transition kernel, preserving the $H^3\\varepsilon^{-2}$ dependence. A complementary uniform guarantee for all bounded rewards yields the state-dimension saturation. We establish lower bounds matching up to logarithmic factors through a rare-exit construction with subset rewards and action encoding. These bounds apply to adaptive simulator queries and arbitrary randomized history-dependent output policies, while the upper bounds are attained by deterministic stationary policies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05562",
  "author_total": 1,
  "authors": [
    {
      "name": "Yue Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2k9p0mb7w76kb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05562",
  "fulltext_url": null,
  "id": "2k9p0mb7w76kb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05562",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05562",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2k9p0mb7w76kb.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:06Z",
      "native_id": "2611.05562",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05562"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Near-Minimax Sample Complexity for Multi-Objective Reinforcement Learning under Generative Models",
  "title_text": "Near-Minimax Sample Complexity for Multi-Objective Reinforcement Learning under Generative Models",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:32Z",
  "url": "https://research.draconitic.com/paper/2k9p0mb7w76kb",
  "venue": "arXiv",
  "versions": []
}