{
  "abstract": "We study an unknown-transition finite-horizon Markov decision process (MDP) with a finite collection of known reward functions $\\{r^1, r^2, \\ldots, r^M\\}$. The goal is to output an $ε$-optimal policy for every reward using online episodic interaction only. Performance is measured by the policy error $V_{0}^{*, m} - V_{0}^{\\widehatπ^{m}, m}$ where $m\\in [M]$ represents the reward function and $V_{0}^{*, m}=\\mathbb{E}_{s_1\\sim μ}[V_{1}^{*, m}(s_1)]$. Under this setting, we design a provably efficient algorithm to establish a minimax sample complexity bound of $$ O\\left(\\frac{SAH^3}{ε^2}\\log M \\mathrm{polylog}\\left(\\frac{SAH\\log M}{\\min\\left\\{ε, 1\\right\\}δ}\\right)\\right)$$ episodes, with no additional burn-in cost. This matches the information-theoretic lower bound up to a factor of $ \\mathrm{polylog}(SAH\\log M/(\\min\\left\\{ε, 1\\right\\}δ))$. Our method combines three technical ingredients. First, we adapt MVP to reward-switching learning to construct optimistic value estimates. Second, we use fresh replay samples to conservatively evaluate the candidate policies. Third, gap-based multiplicative weights updates adjust the reward-sampling distribution using the differences between these estimates, converting weighted learning progress into simultaneous guarantees for all rewards.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36486",
  "author_total": 2,
  "authors": [
    {
      "name": "Zijun Chen"
    },
    {
      "name": "Zihan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/20ws683dfckgj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36486",
  "fulltext_url": null,
  "id": "20ws683dfckgj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36486",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Reinforcement Learning in Robotics"
    ]
  ],
  "openalex": "W7214948301",
  "pdf_url": "https://arxiv.org/pdf/2609.36486",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/20ws683dfckgj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:41Z",
      "native_id": "2609.36486",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36486"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Optimal Multi-Reward Reinforcement Learning",
  "title_text": "Optimal Multi-Reward Reinforcement Learning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:41Z",
  "url": "https://research.draconitic.com/paper/20ws683dfckgj",
  "venue": "arXiv",
  "versions": []
}