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To reduce verifier hacking, many RLVR systems binarize rewards to $\\{0,1\\}$, but imperfect verifiers inevitably introduce \\emph{false negatives} (rejecting correct answers) and \\emph{false positives} (accepting incorrect ones). We formalize verifier unreliability as a stochastic reward channel with asymmetric noise rates $\\rho_0$ and $\\rho_1$ -- the FP rate and the FN rate, respectively. From this abstraction we derive two lightweight corrections: (i) a \\emph{backward} correction that yields an unbiased surrogate reward and thus an unbiased policy-gradient estimator in expectation, and (ii) a \\emph{forward} correction that reweights score-function terms so the expected update aligns with the clean gradient direction and requires only the FN rate. We implement both as lightweight hooks in a group relative policy optimiz","title":"Reinforcement Learning with Verifiable yet Noisy Rewards under Imperfect Verifiers","url":"https://arxiv.org/abs/2510.00915","vendor":"arxiv_cs_ai"},"summary":"arXiv:2510.00915v4 Announce Type: replace-cross \nAbstract: Reinforcement Learning with Verifiable Rewards (RLVR) replaces costly human labeling with automated verifiers. To reduce verifier hacking, many RLVR systems binarize rewards to $\\{0,1\\}$, but imperfect verifiers inevitably introduce \\emph{false negatives} (rejecting correct answers) and \\emph{false positives} (accepting incorrect ones). We formalize verifier unreliability as a stochastic reward channel with asymmetric noise rates $\\rho_0$ and $\\rho_1$ -- the FP rate and the FN rate, respectively. From this abstraction we derive two lightweight corrections: (i) a \\emph{backward} correction that yields an unbiased surrogate reward and thus an unbiased policy-gradient estimator in expectation, and (ii) a \\emph{forward} correction that reweights score-function terms so the expected update aligns with the clean gradient direction and requires only the FN rate. We implement both as lightweight hooks in a group relative policy optimiz","title":"Reinforcement Learning with Verifiable yet Noisy Rewards under Imperfect Verifiers","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-25T04:43:48Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2510.00915"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:b7bdb0222a8a26a1259046656173c3576fe27295c2dd62e99d660b33788b3cc2e3d252d42391ff2030deb891f957e80aa68c5bbff5fadf39b034de284ae8a309","signer":"crovia.substrate","subject":{"observed_at":"2026-05-25T04:43:48Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2510.00915"},"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":"f04cdb833084a575fa7daa7ffa9d21a6288007adf3a577c0e5055cfcfa776348","leaf_index":149705,"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":"818f1ef1d240f633640f0a696e8fc9e37727d98d90fdd4e6e9039ad0ffaae071","side":"left"},{"sibling":"cf1fed66230d460c57f33c3954261465290fb70059647e91efbb7b0b008b4a90","side":"right"},{"sibling":"bad44562311bc93e1f6b09d0d00f2ed472efccb47cf449c33a5b47baf798be7f","side":"right"},{"sibling":"89707db1d69f3c5a52317d87cbfb21b4ac24392ff8de657d2f275981a072fd21","side":"left"},{"sibling":"ea2b5b523c5dd2806f55b9366dfeb28dbf92cbe65f63fadc21212b1f242f8d3d","side":"right"},{"sibling":"71332b767201373a22f07734e56c280aca2f5c4843249e6b798501f1aaebcd42","side":"right"},{"sibling":"9a9dec70c246f07136fd93efad0647d42e469fcfca31c6741dcb1d715bd9ce45","side":"left"},{"sibling":"cb71a04113e54ec457f452a34b2778696e1747afe98ba9da255ce1f5fd8619d7","side":"left"},{"sibling":"e044acc52c31efe134c902c984299ea3452b42df993d096ed61ad8be9d530bbc","side":"right"},{"sibling":"6be461ecf12dedf98a31921aa7b5c32d4a32df6897e0f697b8bf1a4ba3e2d324","side":"right"},{"sibling":"c2861a8cef3eb66bf2726aa377c24a6bf6e8b7489dcd0e870b61d62a35ccadfb","side":"right"},{"sibling":"134949308b15cffd6792ee2cf678119af34d69a64764d7c89cd47573c94e1cda","side":"left"},{"sibling":"debbc1a6232ea7970009b91bdc2345041b2de5ac59551f955855d579001e512c","side":"right"},{"sibling":"216869846f40bd905626884f58cb67b9019e488b3656946a7808c436ab7339ac","side":"right"},{"sibling":"35ca36cee447f0ef7064a25d55f59357c66901e31427729c4c1d8b14aa8adb6c","side":"left"},{"sibling":"e734b0c6d6d13acb5f4cf00367b3913e5bbf1aa717377aa4e4820c6de24b7673","side":"right"},{"sibling":"4bbb7f78e96179bb9cdd06d7207b66b3503ab68e4880438263025b04ebe8f7ec","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":149835,"merkle_root":"51484a548bc0cf3d178eec868e98935c87f0aa83369143b7c96b048585e5ba01","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260525T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-25T05:37:33Z","sig_algorithm":"ed25519","signature":"99a657e53a015ace0bade5d7fbb3f60f950b6d1e1128251a63afcc454a492422cae5efdc0c18503b4f7e62f371bd48f2889be78d9048c4681d6c1e73f754d705","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_8c40392129db241d5b37777034723c53024759ba885325559b4b4edfca8c4927"}}