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Existing algorithms for MNL mixture MDPs yield a regret of $\\smash{\\tilde{O}(dH^2\\sqrt{T})}$ (Li et al., 2024), where $d$ is the feature dimension, $H$ the episode length, and $T$ the number of episodes. Inspired by the logistic bandit literature (Abeille et al., 2021; Faury et al., 2022; Boudart et al., 2026), we introduce a problem-dependent constant $\\bar\\sigma\\_T \\leq 1/2$, measuring the normalised average variance of the optimal downstream value function along the learner's trajectory. We propose an algorithm achieving a regret of $\\smash{\\tilde{O}(dH^2\\bar\\sigma\\_T\\sqrt{T})}$, which recovers the existing bound in the worst case and improves upon it for structured MDPs. For instance, for KL-constrained robust MDPs, $\\bar\\sigma\\_T = O(H^{-1})$, reducing the horizon dependence by a factor ","title":"Minimax Optimal Variance-Aware Regret Bounds for Multinomial Logistic MDPs","url":"https://arxiv.org/abs/2605.19768","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.19768v1 Announce Type: new \nAbstract: We study reinforcement learning for episodic Markov Decision Processes (MDPs) whose transitions are modelled by a multinomial logistic (MNL) model. Existing algorithms for MNL mixture MDPs yield a regret of $\\smash{\\tilde{O}(dH^2\\sqrt{T})}$ (Li et al., 2024), where $d$ is the feature dimension, $H$ the episode length, and $T$ the number of episodes. Inspired by the logistic bandit literature (Abeille et al., 2021; Faury et al., 2022; Boudart et al., 2026), we introduce a problem-dependent constant $\\bar\\sigma\\_T \\leq 1/2$, measuring the normalised average variance of the optimal downstream value function along the learner's trajectory. We propose an algorithm achieving a regret of $\\smash{\\tilde{O}(dH^2\\bar\\sigma\\_T\\sqrt{T})}$, which recovers the existing bound in the worst case and improves upon it for structured MDPs. For instance, for KL-constrained robust MDPs, $\\bar\\sigma\\_T = O(H^{-1})$, reducing the horizon dependence by a factor ","title":"Minimax Optimal Variance-Aware Regret Bounds for Multinomial Logistic MDPs","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-20T04:43:44Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.19768"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:8afe602b3f0c2841c3ebf147b68bafbe335542ef543ace18f21e5b120c85455579b67bfe3f8c58b2ebd8be1a1794816e5f17d454456ce0a45f10307ea206160a","signer":"crovia.substrate","subject":{"observed_at":"2026-05-20T04:43:44Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.19768"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"7128f936824f4eebdb9147ad148f1a24efa1706ccc4b8ce7058e69ef5de531ff","leaf_index":144945,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"2c95443e504ee23abf00dcf0730c596b81691badf6e3e1d3ebdbc702174555e2","side":"left"},{"sibling":"b219786b925011596226a0fa08b6cf1c9cdce321bbcb824dc50b47a8a005cdec","side":"right"},{"sibling":"40b66889a86dcbe4b6e6aad68f0d9227b81b78d34e2ef04f24632861e2b082e1","side":"right"},{"sibling":"ffae2275eb6ffe16d0f7e21523316cabc0f943272ba65eed7d641fb44985d416","side":"right"},{"sibling":"bfeaf28695bd8c79f771993181ca36060909a2cbb38e51f59dfe7c16489f5258","side":"left"},{"sibling":"1d9a53b793767d0e949dedec96b7e681027abc3dbbb461606fe118def9d7d4ab","side":"left"},{"sibling":"9dfea8c2063a3b5da665f6432f8c0c081d0ea279aadf5f27f222e6b1ef5cc4eb","side":"right"},{"sibling":"5c26ec91378ced2564bd7218068bacda3ade3a0517e2dc081e9d169a340044ba","side":"right"},{"sibling":"9db04d2181fb869f16a5baf7dcfe999cc93a7e9beef8493d0cc71f57470fe5e1","side":"right"},{"sibling":"1526885f19d1fadf6955cf519dbc4e62d593a4bba99d741e8c301740a7068233","side":"left"},{"sibling":"e3a7d5c07f161682d61bd453ffc02ecdf87cfeda70f986d6650017f9d2d6b265","side":"left"},{"sibling":"edbc49f08e5b92291934c05c9e6efd270a6b0698d8d2fa474006366027dfe098","side":"right"},{"sibling":"3e4df6e7457cecbf36f350375e72dcab336a3984422e4c406ef809e4e2944e96","side":"left"},{"sibling":"8f4c0fbe56b6c010fbb8c782ebcd478079bb3f991d8704e2534209a075d9163c","side":"left"},{"sibling":"be08fedc4e72a6fb56606f66812fae7317e09690b9acb18385f4ab117a981238","side":"right"},{"sibling":"0534329a7475dc9df51998c83c16892126679dade0fa34182f21e869599386c7","side":"right"},{"sibling":"2d24720928ead0e7670650eb55f558c4f20e4c18df376f47ba72cfa8cf0ed344","side":"right"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":147301,"merkle_root":"08903d7159c3b38eeeeafc09eab15139ea417f1d94f02f1fbc87296b37db840a","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260521T183701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-21T18:37:33Z","sig_algorithm":"ed25519","signature":"905f2924632dfa2970c8690285f5b5d4a1d891d0e0ef1cbc404ebec2fd937215ac768e16f0a9f28b18977a55ae0bfd226db6833ae7ef588729054117d2da7303","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_6ad3b08a8dffa7d9407aa980025bc155a8d56aee10c0ab6f6fada9dcae5bd35c"}}