{
  "abstract": "Reinforcement learning (RL) agents deployed in real-world environments are often vulnerable to adversarial perturbations in state observations, creating risks in safety-critical applications. Certification methods can improve robustness against adversarial perturbations by providing lower bounds on expected cumulative rewards. Existing certification methods, however, mainly focus on risk-neutral objectives. In this paper, we extend certification methods to risk-sensitive objectives by establishing lower bounds on the exponential utility of cumulative rewards under $l_{p}$-norm-bounded state adversarial perturbations ($1\\leq p <\\infty$). By introducing a $ϕ$-divergence relaxation of the perturbation set, we formulate the risk-sensitive certification problem as a convex optimization and derive its dual to obtain a tractable approximation of the certified lower bound. We further propose an empirical method that improves certified lower bounds by selecting the training risk-aversion parameter $β$ independently of the risk level used during evaluation. Experiments on both OpenAI Gym environments and a machine replacement problem show that, compared to risk-neutral training, risk-averse training generally yields policies with higher certified lower bounds, particularly under larger perturbation budgets. Moreover, under both risk-neutral and risk-averse evaluation settings, increasing risk aversion during training leads to non-monotonic certification performance, where certified lower bounds initially improve but eventually decrease due to overly conservative policies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10866",
  "author_total": 3,
  "authors": [
    {
      "name": "Tong Li"
    },
    {
      "name": "Saunak Kumar Panda"
    },
    {
      "name": "Yisha Xiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b63nj18ys83af.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10866",
  "fulltext_url": null,
  "id": "b63nj18ys83af",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10866",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Adversarial Robustness in Machine Learning"
    ]
  ],
  "openalex": "W7212282269",
  "pdf_url": "https://arxiv.org/pdf/2609.10866",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b63nj18ys83af.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10866",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10866"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Certifying Lower Bounds for Risk-Sensitive Reinforcement Learning under Adversarial State Perturbations",
  "title_text": "Certifying Lower Bounds for Risk-Sensitive Reinforcement Learning under Adversarial State Perturbations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/b63nj18ys83af",
  "venue": "arXiv",
  "versions": []
}