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Recent work addresses this by evaluating the sequence of per-round expected rewards through the generalized $p$-mean, interpolating between utilitarian welfare ($p=1$), Nash welfare ($p\\to0$), and Rawlsian fairness ($p\\to-\\infty$). Although tight guarantees are known for $p\\ge0$, the strictly fair regime $q=-p>0$ remains unresolved because negative-power means are dominated by the smallest per-round rewards.\n  For $\\sigma$-sub-Gaussian rewards with nonnegative means, the best prior algorithm relied on uniform early exploration and achieved regret $O(k^{(q+1)/2}/\\sqrt{T})$, while the only general lower bound was the classical $\\Omega(\\sigma\\sqrt{k/T})$. Thus it was unclear whether the extra dependence on $k$ was intrinsic to strict fairness or ","title":"Price of Fairness in Bandits: A Tight Minimax Characterization","url":"https://arxiv.org/abs/2607.13402","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.13402v1 Announce Type: cross \nAbstract: In bandit problems, standard regret-minimizing algorithms treat exploration as an amortized cost, which can expose early participants to unfair ex-ante losses in settings such as clinical trials. Recent work addresses this by evaluating the sequence of per-round expected rewards through the generalized $p$-mean, interpolating between utilitarian welfare ($p=1$), Nash welfare ($p\\to0$), and Rawlsian fairness ($p\\to-\\infty$). Although tight guarantees are known for $p\\ge0$, the strictly fair regime $q=-p>0$ remains unresolved because negative-power means are dominated by the smallest per-round rewards.\n  For $\\sigma$-sub-Gaussian rewards with nonnegative means, the best prior algorithm relied on uniform early exploration and achieved regret $O(k^{(q+1)/2}/\\sqrt{T})$, while the only general lower bound was the classical $\\Omega(\\sigma\\sqrt{k/T})$. Thus it was unclear whether the extra dependence on $k$ was intrinsic to strict fairness or ","title":"Price of Fairness in Bandits: A Tight Minimax Characterization","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-16T04:44:04Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.13402"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:5e58a7ac0ef2ea114c3820d1fac677e1be29ffc9c7b0e760c08675ae39d655bc45086275bfc527249b881132e36394825461de11c3c5f978780158466d14290c","signer":"crovia.substrate","subject":{"observed_at":"2026-07-16T04:44:04Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.13402"},"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":"6a8eb464383e10898e3158320c079f363e2c97b6ff67f8271b48cf027ae8c84a","leaf_index":319824,"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":"9c1ec6949d3b09d5eab71af384035a8006bccd99f216aab8928cf49d9213545d","side":"right"},{"sibling":"da018e561284fb6fa63d19587f614690340f1e6f41e067690880cf8ff076358e","side":"right"},{"sibling":"fab884e9dfd3e24f2c73c7a977901e00d30634cfcda016a610d3486277b76d7b","side":"right"},{"sibling":"556bcdc521601e5496542dd1635a0fc62a981c70ddb3bc66d48802d31f65ba02","side":"right"},{"sibling":"0a0b942f846b9605e61fa96d154bb8f3a77c10e55695a5b38993290f481f4684","side":"left"},{"sibling":"d4883068a918de3912db61033720014f921694c62ea82aab5e7e249915b74ffd","side":"right"},{"sibling":"2c7004d4be02967141b4e5609671d597ca4f0e246e61da911ae67ca20ab6e7e7","side":"left"},{"sibling":"ec3fec9bb698cfe3c65d9f75111532c318eaa7e7c5b933ded046cea471e330ab","side":"right"},{"sibling":"929619d7bb5abd9d4c015f749565f8d43a371ed382bafe122457d67edb9b8323","side":"left"},{"sibling":"1290775fa2a1fe2079ed83a9c60b8cb479714b6312967daa62f6a91dbbe1cac9","side":"right"},{"sibling":"95977bf2fb44d423026e874e6c275f78b1cf48666d2c472c5e4603d16f4faf7f","side":"right"},{"sibling":"6b83879fdb76b5b7270071f1edfe4d1a059fa9b92653e70fc8c8893214b8f237","side":"right"},{"sibling":"ff49c1d8749b258f58cc33cfaf20d723098ed6860fb62a6779db960d6250915b","side":"right"},{"sibling":"34d85f6ad6cc7dfa79d90e2b9ff99a561bcdc75b0301bbbd3e83861f54535c1e","side":"left"},{"sibling":"f302542c38ba7c3aab7c9280dd60259ecec777dca6e6f71b6f0729b0b8791b72","side":"left"},{"sibling":"d8b9143917b539c543cf4448cec00131f8b807bd8004979c54ebe09798748c66","side":"left"},{"sibling":"3ee6ab8db1878db0b324dd807ca233edd472899b8e90d2c5e018848ea5d12d99","side":"right"},{"sibling":"73a8d1605c15a74de720f0c54b5b4567e3eb8b5999bd8812dc66eedc461540fa","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","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":320080,"merkle_root":"1e159bceacfdb1f3c930dae410f8759ddc4c762abcfa4a257b150d6f44ab16e0","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260716T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-16T05:38:31Z","sig_algorithm":"ed25519","signature":"c1cd1fc5704d4fec4dee47b29a0e9877f8cfb41eb61dcfd783d82344a15f6e44d80d6cd5128849547b62fe9d9724fc71433319ab6030445b4ac1c9e6bf8a3709","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_bbec0a8e88c55b0b6a8ff5acfdfceab0bd8a2c0ce04229b5532f17d8a41a6d1b"}}