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Nevertheless, the exact sample complexity of KL-regularized offline learning remains largely from fully characterized. In this paper, we study this question in the setting of multi-armed bandits (MABs). We provide a sharp analysis of KL-PCB (Zhao et al., 2026), showing that it achieves a sample complexity of $\\tilde{O}(\\eta SAC^{\\pi^*}/\\epsilon)$ under large regularization $\\eta = \\tilde{O}(\\epsilon^{-1})$, and a sample complexity of $\\tilde{\\Omega}(SAC^{\\pi^*}/\\epsilon^2)$ under small regularization $\\eta = \\tilde{\\Omega}(\\epsilon^{-1})$, where $\\eta$ is the regularization parameter, $S$ is the number of contexts, $A$ is the number of arms, $C^{\\pi^*}$ policy coverage coefficient at the optimal policy $\\pi^*$, ","title":"On the Optimal Sample Complexity of Offline Multi-Armed Bandits with KL Regularization","url":"https://arxiv.org/abs/2605.02141","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.02141v1 Announce Type: cross \nAbstract: Kullback-Leibler (KL) regularization is widely used in offline decision-making and offers several benefits, motivating recent work on the sample complexity of offline learning with respect to KL-regularized performance metrics. Nevertheless, the exact sample complexity of KL-regularized offline learning remains largely from fully characterized. In this paper, we study this question in the setting of multi-armed bandits (MABs). We provide a sharp analysis of KL-PCB (Zhao et al., 2026), showing that it achieves a sample complexity of $\\tilde{O}(\\eta SAC^{\\pi^*}/\\epsilon)$ under large regularization $\\eta = \\tilde{O}(\\epsilon^{-1})$, and a sample complexity of $\\tilde{\\Omega}(SAC^{\\pi^*}/\\epsilon^2)$ under small regularization $\\eta = \\tilde{\\Omega}(\\epsilon^{-1})$, where $\\eta$ is the regularization parameter, $S$ is the number of contexts, $A$ is the number of arms, $C^{\\pi^*}$ policy coverage coefficient at the optimal policy $\\pi^*$, ","title":"On the Optimal Sample Complexity of Offline Multi-Armed Bandits with KL Regularization","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-06T04:43:18Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.02141"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:c8f95b203b9540112230e67673a75c5c121e401450979ecd0dc9b3af8dec529113c3d0d11010172c9c3b0216b37d230ad80497e9f3f903ded36e67a4f7aae301","signer":"crovia.substrate","subject":{"observed_at":"2026-05-06T04:43:18Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.02141"},"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":"caea29af8596d0f0ce380398fa3c4dfda7ee6c9a3021772d6874416f8655d25e","leaf_index":116329,"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":"d926d741fdd8df1d0680e3c87cd6916dd7f52be54b2fdf1a40c85c8b47471314","side":"left"},{"sibling":"7a2839f43d6bc636f182106f4510c09aa3b3f05d22e9f3cacdf53caaa2df61d1","side":"right"},{"sibling":"a765036924b0cf4754c4a9cc63b886df238a98e8baa678f1a906d21503df6eeb","side":"right"},{"sibling":"cd07c8d034ea121cb47b43b60e089c0a99f72b17d0c10f2f8db8a61dc75fd4e8","side":"left"},{"sibling":"f4afa9c4fdf9512b81011abff155f8d745d738055216c6270357a177927159b6","side":"right"},{"sibling":"1520586bfd4793dc79a128f0850786d392c8af1a7e3e5f9fdeeabdde90ee49b9","side":"left"},{"sibling":"ad3a284c05693695f2eb1381482f2a0de6f97623fdcf5a64fcab04a5e47aac4a","side":"left"},{"sibling":"29a1d68ae3b47209a045f8f53476ebb8528406538f56ab779e7eb4bfc2794b92","side":"right"},{"sibling":"7a43f13f6340a269b939be4b6e73a199a4e8061f0cf9dbb9ba629243174142d3","side":"right"},{"sibling":"c750384c973eaf46aa237cdabe7a75729862dd4101dca10cb8e0626e0ec2d34a","side":"left"},{"sibling":"ddc060ac400459417799f688c75d5b271636afa40d89ec7fc98652473a8061f6","side":"left"},{"sibling":"282afa51266e47629e34d808a360bbb276348bcc5a24bdcc93e83a76e580293e","side":"right"},{"sibling":"05f89b32c00462e60adf95c1fe4579cdc2791b36e8b17573d8f3b5fd5da95a0b","side":"right"},{"sibling":"8ccd9937a2c0d5c04044d07d1557791b7d07bb31eac41a39a675608d44b38f23","side":"right"},{"sibling":"3a5e69cf0803f4c91f3895ed7c9a95748fef240bec4422e167c05300f79f06c0","side":"left"},{"sibling":"f2817ab288b5324fe49770372c7a10f33f7cd11005f8d4c0a730316f5229dc98","side":"left"},{"sibling":"725fac972e772ca0dc598810ea1abc70df472f72d2d6ab8a0baee2b80e5d2f4c","side":"left"},{"sibling":"98fc57dfef8873b512edc8340f7181df57302bb96777625e072235c62d7c5895","side":"right"}]},"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":134292,"merkle_root":"77fc9c28fae777b81da5b495b3115474df6592dfac590333213d3bdf8b94a9b3","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260515T023701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-15T02:37:25Z","sig_algorithm":"ed25519","signature":"68107a834b00b24f5d4501e5ec727445311f132a486567ecc4c72a4e6dff24c8c21f2de3105293353ba5fdbe370d032819af6aa70f694e2e39b6af6737507009","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_ae29ee9d4d38e08187e9d92c5b3c462f5b37c827f8b1f18fee62f750f9f57332"}}