{
  "abstract": "We study the control of Markov decision processes in which the quality of a policy is evaluated by a dynamic, time-consistent Markov risk measure rather than by an expected discounted cost. The main obstacle to combining such measures with reinforcement learning is that a transition risk mapping depends on the transition kernel in a nonlinear way, and therefore cannot be estimated from a single observed transition. We remove this obstacle by employing mini-batch transition risk mappings: the mapping is applied to the empirical measure of $N$ independent next-state samples, and the result is averaged. The resulting mapping is again coherent. However, as an expected value of a function of $N$ next-state values, it admits an unbiased one-sample estimator. We embed this mapping into a double deep Q-network, analyze the two sources of estimation bias that arise, and obtain a risk-averse Q-learning method applicable to state spaces far beyond the reach of tabular schemes. The method is applied to an underwater robot navigation problem, in which a vehicle must visit collection points, gather stochastic information payloads, and deliver them at transmission points, while exposed at each step to the risk of destruction. A hierarchical decomposition delegates path execution to an exact graph search and confines learning to the high-level ``collect or transmit'' decision. A low-dimensional feature map, invariant under the symmetries of the problem, replaces the raw state--configuration encoding. In experiments on $300$ held-out environments, the resulting policies transfer to instance sizes never seen in training, and already $N=2$ reduces the upper semideviation of the outcome distribution while simultaneously improving its mean whenever the simulator is misspecified---an empirical counterpart of the duality between coherent risk measures and distributional robustness.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07998",
  "author_total": 2,
  "authors": [
    {
      "name": "Aayush Patel"
    },
    {
      "name": "Andrzej Ruszczyński"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ejsfz0v43hjea.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07998",
  "fulltext_url": null,
  "id": "ejsfz0v43hjea",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07998",
  "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.AI"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Reinforcement Learning in Robotics"
    ]
  ],
  "openalex": "W7212037684",
  "pdf_url": "https://arxiv.org/pdf/2609.07998",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ejsfz0v43hjea.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07998",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07998"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Mini-Batch Risk-Averse Deep Q-Learning: A Robot Navigation Case Study",
  "title_text": "Mini-Batch Risk-Averse Deep Q-Learning: A Robot Navigation Case Study",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/ejsfz0v43hjea",
  "venue": "arXiv",
  "versions": []
}