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Our framework reveals these dualities as arising from a single construction, unifying methods developed separately across reinforcement learning, control, and decision theory.","title":"Generalised Bellman recurrence and three dualities in sequential decision-making","url":"https://arxiv.org/abs/2607.18077","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.18077v1 Announce Type: cross \nAbstract: What gives the Bellman equation its form? We show that the recursive properties of optimal value functions follow from three conditions: that the dynamics decomposes through sufficient statistics, that the return decomposes recursively, and that the aggregation of uncertainty is compatible with both. When all three conditions hold on a common state, the Bellman equation arises from their mutual consistency; when one fails, tractability can often be recovered by augmenting the state or by deforming return or dynamics. The same conditions are shown to give rise to three dualities: one between probability and return, one between return and aggregation, and one between aggregation and probability. Our framework reveals these dualities as arising from a single construction, unifying methods developed separately across reinforcement learning, control, and decision theory.","title":"Generalised Bellman recurrence and three dualities in sequential decision-making","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-21T04:43:35Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.18077"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:e4667a9faec312832e6b04493854d2adf9c4d58cf84e85c34a4924bf4c3d460d60f4156f1f608f20feb94171b242ecba1e599aea2a736be1b2e3875b3081d50b","signer":"crovia.substrate","subject":{"observed_at":"2026-07-21T04:43:35Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.18077"},"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":"80ddeec1b23dde966c2ec6f26061b49e6c397cf9067cf5c8e9bd6d80c3bf050a","leaf_index":336837,"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":"5e9af7ac629d4d2785d87ab5441a1b28026e589b5eedb57873c5f1e5f418f919","side":"left"},{"sibling":"27ebe347935d174e68d8e93817ff62d6cb0208061091f2165207455e5ce5b59b","side":"right"},{"sibling":"b050d9575844e673560207fe14581c791473d1939ddfe6c47861210b4fd8ed9c","side":"left"},{"sibling":"86d30634d60c9d9b6bd621f089a4d3ddf70fe58e0abecc250ea08e957c7d0aca","side":"right"},{"sibling":"830f02ab6185af447c52be9681251b94155e09013a7878c8712a1ccabae54ff7","side":"right"},{"sibling":"ca554dfa6a8758a7105fc0a5770c49c50d6002f56c5e5386b8055fbfbe8c43dd","side":"right"},{"sibling":"ce03a7473ecb89a8a8b71de92b9d2d6aa1aa165b6c59cefc86a37241b7f55b64","side":"left"},{"sibling":"90ee1b815719c44a83e23429473a176437135319947bc07c6e3752315a40068d","side":"left"},{"sibling":"bd233cee8c0876447824d86de33608c36e3a8e17dca0737155291ed768cf56d1","side":"left"},{"sibling":"7b927551b5db06b6571913b4e6792ffcce5291a3eca5a0df4a3b6e296271105f","side":"left"},{"sibling":"b77a0b5ae4607c8fe6ba73449d46b35076e3dedc0c82a2c65a05780d42a7bc2e","side":"right"},{"sibling":"9eb5077edfb3dc553857d4794b925bfce117e0f8a1d049af5d0dd9026b470eef","side":"right"},{"sibling":"414b1a70fd1dcb25489a194714b97492b066684b15d0b7a48a176c4b9b5bc713","side":"right"},{"sibling":"21d66dd41003813f710b7617944f1bfba3258658a5d3370c21cad8f9e945bc99","side":"left"},{"sibling":"613f015699131eb89bd755dee67133be95af25cf5f16c1c8ce4b99d963b8dd86","side":"right"},{"sibling":"a729b574b1135956436ded5eef1fe8f08014ff6a0729749d307ab1bca93fcdc9","side":"right"},{"sibling":"77025bcb374a7ad74f520643e20a8ae1205a7ee78507b0beb93117760f1c29d3","side":"left"},{"sibling":"4bf21052e085e8ac81f1dec1d2b310bd12bf948992de6177d12e9d2fda8d39f0","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":337144,"merkle_root":"5e969cc01afa67e4dbe5d37b712cdb10f4aa1fd74404e02eab724cf487c8d6d9","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260721T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-21T05:38:38Z","sig_algorithm":"ed25519","signature":"5c0c1a8dd2793d787ccd5e49e8b4d70eed136352555518589f05c74be357fc171702e42a76c3a556d90e3d51ff36cb3d292aaac83c66566de7b943f318bda50c","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_7f8352c930d5ac8f4b11e79a5a499944c161e4ab8db00fed83efe0aad06b134c"}}