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A natural mitigation is \\emph{pessimism}: penalizing rewards in regions where the RM is uncertain. However, standard scalar RMs provide no principled notion of uncertainty. We argue that the right object is a \\emph{distributional} reward model $p(r\\mid x,y)$. Under either a Bayesian inference or a KL-distributionally robust optimization (KL-DRO) lens, the KL-regularized RLHF objective admits a closed-form effective reward $\\tilde r(x,y) = \\pm\\beta\\log\\mathbb{E}_p[e^{\\pm r/\\beta}]$. The pessimistic branch unifies the prior heuristics for RM ensemble aggregation: mean aggregation, worst-case optimization (WCO), and uncertainty-weighted optimization (UWO) all emerge as limits or truncations of this single expression. This also cl","title":"A Unifying Lens on Reward Uncertainty in RLHF","url":"https://arxiv.org/abs/2606.09073","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.09073v1 Announce Type: cross \nAbstract: Reinforcement learning from human feedback (RLHF) is bottlenecked by \\emph{reward hacking}, where the policy exploits errors in a proxy reward model (RM) and produces high RM scores without genuine quality gains. A natural mitigation is \\emph{pessimism}: penalizing rewards in regions where the RM is uncertain. However, standard scalar RMs provide no principled notion of uncertainty. We argue that the right object is a \\emph{distributional} reward model $p(r\\mid x,y)$. Under either a Bayesian inference or a KL-distributionally robust optimization (KL-DRO) lens, the KL-regularized RLHF objective admits a closed-form effective reward $\\tilde r(x,y) = \\pm\\beta\\log\\mathbb{E}_p[e^{\\pm r/\\beta}]$. The pessimistic branch unifies the prior heuristics for RM ensemble aggregation: mean aggregation, worst-case optimization (WCO), and uncertainty-weighted optimization (UWO) all emerge as limits or truncations of this single expression. This also cl","title":"A Unifying Lens on Reward Uncertainty in RLHF","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-09T04:43:45Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.09073"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:a8531c0930924312599c9f56bbbb67f2b1243462b2059755152f027f0019a700c872ff2d0995c7e6052fd210610a847f13b58c672ce17a55d4abcce98c01f90a","signer":"crovia.substrate","subject":{"observed_at":"2026-06-09T04:43:45Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.09073"},"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":"e82dec0693d24d831951b2128cc8ee208ff7c51272d8c721aabe63e9b19b9827","leaf_index":224359,"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":"954b66837950362d8e7acc86cfb17610fa39b20f2adea7fb3fe351d2559167d8","side":"left"},{"sibling":"a4530dfcef6c2f346220246c7cf770fbe5ada4491d8b4db457cc71a72d7935a4","side":"left"},{"sibling":"6ec286eab9c02b07060d901d580379d681b402084e0a42fd260df6f313c5dfde","side":"left"},{"sibling":"7231c4271858188f9dfef628b25e22ef392dc16b0497ea70e807aeb1f5aac4d6","side":"right"},{"sibling":"f999d3370c14465e8dc5cc3e5e3fcf85b37a679670c20f034e42fa0c97cf64d7","side":"right"},{"sibling":"c5907755da51f473c63329cbd3194ceddf1f05a503901a2415386882a121ff37","side":"left"},{"sibling":"f0a492f36de5d4a50581f2f490a2e1704c68ff29d4b921f427506dbbc19159fc","side":"left"},{"sibling":"6aee4d57225362b2670992e69503217771be95795abcdc0a9d9022571196aa2b","side":"right"},{"sibling":"f6fb234a4e2f067b22329eec05b093a8b38f0411de9434d5a8eb55c2f70f1a2f","side":"right"},{"sibling":"b2df6a4bb3e928f0b447931cc688ae01d2415773a2b07cfed0b1cba689078aed","side":"right"},{"sibling":"b1c9ec856caa0fd46bb47b46f18c59ebcd295d774ca17adb3b46f05d394a6a5d","side":"left"},{"sibling":"24fdc29d461691aedb6fa920758206b5bb43851f477ef7a04c34aaed84b8971b","side":"left"},{"sibling":"036922da4e1e2c46d948f070454bfad299b7406fb00735ea9d8bd1e687f5f445","side":"right"},{"sibling":"533d82482604463aa4a281b9d8b85917b383b7c5f924b2b494039524c55e8797","side":"left"},{"sibling":"b2590791b920ca2a4ed39de126d2c0b1a10d9e7e62f572f12425f214e767b6e1","side":"left"},{"sibling":"87c6b850dfec08ac35a693d9db3a3315250a68adb1cfab9b1015f212b63b15bd","side":"right"},{"sibling":"c300cf0154c136afc09b1702a0be98f4ba5b6dc5cf57e8cc714ec1eaf4196eff","side":"left"},{"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":224761,"merkle_root":"e9f7b49b652e869ab97ffba9c5a31356b2d0e3dc5d00bb28944adf737c46b1e7","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260609T103805Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-09T14:15:34Z","sig_algorithm":"ed25519","signature":"8ad8076fb12c8e486ae1d1559a9a7ba8e2ee996a9ad3d8ba7bcdbdbd88ab3a15bcb429707aca6d3e9d8b97e2ba755b3dcc77b1abb6601ccb829842719a6fb30d","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_ef4431380740133f63ca2444e90299875e3843588fbfa454f7e937a5d033b1c9"}}