{
  "id": "1912.01192",
  "version": "v1",
  "published": "2019-12-03T05:04:40.000Z",
  "updated": "2019-12-03T05:04:40.000Z",
  "title": "Learning Adversarial MDPs with Bandit Feedback and Unknown Transition",
  "authors": [
    "Tiancheng Jin",
    "Haipeng Luo"
  ],
  "comment": "14 pages",
  "categories": [
    "cs.LG",
    "stat.ML"
  ],
  "abstract": "We consider the problem of learning in episodic finite-horizon Markov decision processes with unknown transition function, bandit feedback, and adversarial losses. We propose an efficient algorithm that achieves $\\mathcal{\\tilde{O}}(L|X|^2\\sqrt{|A|T})$ regret with high probability, where $L$ is the horizon, $|X|$ is the number of states, $|A|$ is the number of actions, and $T$ is the number of episodes. To the best of our knowledge, our algorithm is the first one to ensure sub-linear regret in this challenging setting. Our key technical contribution is to introduce an optimistic loss estimator that is inversely weighted by an $\\textit{upper occupancy bound}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-03T05:04:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "I.2.6",
      "I.2.6"
    ],
    "keywords": [
      "learning adversarial mdps",
      "bandit feedback",
      "episodic finite-horizon markov decision processes",
      "ensure sub-linear regret",
      "optimistic loss estimator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}