{
  "abstract": "Monte-Carlo Tree Search (MCTS) typically stores only scalar mean estimates, which makes it poorly suited for tail-risk objectives such as conditional value-at-risk (CVaR). We introduce Categorical Thompson Sampling with Optimism (CATSO) and Particle Thompson Sampling with Optimism (PATSO), two distributional MCTS algorithms that maintain finite-support empirical backup laws at Q-edges. CATSO represents Q-edge laws with categorical atoms and Dirichlet Thompson sampling, while PATSO represents them with adaptive particles. Both algorithms select actions using the CVaR of a Thompson-sampled Q-edge law plus a polynomial optimism bonus, and propagate scalar continuation values through visit-weighted averages of child Q-edge CVaR scores. For the finite-depth nested CVaR planning target, we prove an $O(n^{-1/2})$ bound on the root value error after $n$ rollouts, which upper-bounds the risk-sensitive simple regret. CATSO adds a fixed-grid discretization bias, while capped PATSO adds a tunable Wasserstein compression bias. Experiments on stochastic planning benchmarks show that distributional Q-edges improve lower-tail return and reduce catastrophic outcomes when mean-optimal and risk-sensitive behavior differ.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23565",
  "author_total": 4,
  "authors": [
    {
      "name": "Quynh Trinh"
    },
    {
      "name": "Trung Nguyen"
    },
    {
      "name": "Nam Nguyen"
    },
    {
      "name": "Tuan Dam"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f9gf4zpp7m529.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23565",
  "fulltext_url": null,
  "id": "f9gf4zpp7m529",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23565",
  "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",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7222931240",
  "pdf_url": "https://arxiv.org/pdf/2610.23565",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f9gf4zpp7m529.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:43Z",
      "native_id": "2610.23565",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23565"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Beyond Expected Values: Risk-Sensitive Planning with Distributional Monte-Carlo Tree Search",
  "title_text": "Beyond Expected Values: Risk-Sensitive Planning with Distributional Monte-Carlo Tree Search",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:38Z",
  "url": "https://research.draconitic.com/paper/f9gf4zpp7m529",
  "venue": "arXiv",
  "versions": []
}