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Our main result is an exact decomposition: under precisely characterized conditions, the cumulative \\emph{regret} of a dynamic policy equals the sum of per-period covariances between the cost vector and the policy's decision. This extends the single-period identity of Aldridge~(2026) to the full multi-period setting of stochastic dynamic programming.\n  We prove the identity holds exactly under i.i.d. costs and mean-unbiased Markov policies, derive closed-form bias corrections for non-stationary and time-varying cases, and establish the discounted-horizon analog. A Bellman recursion for the covariance regret functional connects the result to standard reinforcement learning algorithms; for rolling-window policies, the estimation-error bias is $O(d/w)$.\n  The decomposition has direct implications for algorithmic auditing in st","title":"Evaluating AI Investment Strategies","url":"https://arxiv.org/abs/2606.08791","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.08791v1 Announce Type: cross \nAbstract: We study the problem of auditing a black-box algorithmic decision-maker from observable inputs and outputs alone. Our main result is an exact decomposition: under precisely characterized conditions, the cumulative \\emph{regret} of a dynamic policy equals the sum of per-period covariances between the cost vector and the policy's decision. This extends the single-period identity of Aldridge~(2026) to the full multi-period setting of stochastic dynamic programming.\n  We prove the identity holds exactly under i.i.d. costs and mean-unbiased Markov policies, derive closed-form bias corrections for non-stationary and time-varying cases, and establish the discounted-horizon analog. A Bellman recursion for the covariance regret functional connects the result to standard reinforcement learning algorithms; for rolling-window policies, the estimation-error bias is $O(d/w)$.\n  The decomposition has direct implications for algorithmic auditing in st","title":"Evaluating AI Investment Strategies","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/2606.08791"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:644494b6f179a17c6c54522506827deca841824f1d09d2e03e4841ed256b71a4c48922a4187b31905f3ca3ef6481e2150f94883a3c654c56c730cb88c9fe960f","signer":"crovia.substrate","subject":{"observed_at":"2026-06-09T04:43:45Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.08791"},"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":"2518f005159267d708b663df975547726197025b1d287d59e9f8d3668616af3e","leaf_index":224325,"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":"7d2d9bbbbe1cdeecacf1310e8f7ffe78ecdf5e665fe87be8e55d6ae2700c2a7e","side":"left"},{"sibling":"131afebf622642a62206d819613e8dd9d2ab27c46d7681e534c0adfeb842d3eb","side":"right"},{"sibling":"dc73e7912c2a38cda2c95920fd13cc7afc17cc86212123cc2f6714f76a87e9ae","side":"left"},{"sibling":"3394ed3e317c024fd1fd005811dbadd3f230af0e9a7b052fb895fececedd57e2","side":"right"},{"sibling":"71dfaa8de4ce108398cb3c62195a47a87f0ffd0fc649b8d12ccae3a7849a25c7","side":"right"},{"sibling":"cac653fa1469e2ebd5ae32b3679c243421d80a3b155a89b34ff132a34528a8dc","side":"right"},{"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_0b980aa18c640be2ed1533c5af8d6b9b91e66ea1ef7cbd1a68e9750499591de7"}}