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Focusing on an all-ones residual correction, we interpret the resulting algorithm through the geometry of switching systems and, to the best of our knowledge, give the first JSR-based convergence analysis of deflated Q-VI for policy optimization problems. Our analysis reveals that the standard Q-VI switching system model has JSR exactly the discount factor $\\gamma\\in (0,1)$, since all admissible subsystems share the all-ones vector as an invariant direction. By passing to the quotient space that removes this direction, we obtain a projected switching system model whose JSR governs the relevant error dynamics and may be strictly smaller than $\\gamma$. Therefore, the deflated Q-VI admits a potentially sharper convergence-rate characterization than the ambient-space $\\gamma$-bo","title":"Switching-Geometry Analysis of Deflated Q-Value Iteration","url":"https://arxiv.org/abs/2605.10811","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.10811v1 Announce Type: cross \nAbstract: This paper develops a joint spectral radius (JSR) framework for analyzing rank-one deflated Q-value iteration (Q-VI) in discounted Markov decision process control. Focusing on an all-ones residual correction, we interpret the resulting algorithm through the geometry of switching systems and, to the best of our knowledge, give the first JSR-based convergence analysis of deflated Q-VI for policy optimization problems. Our analysis reveals that the standard Q-VI switching system model has JSR exactly the discount factor $\\gamma\\in (0,1)$, since all admissible subsystems share the all-ones vector as an invariant direction. By passing to the quotient space that removes this direction, we obtain a projected switching system model whose JSR governs the relevant error dynamics and may be strictly smaller than $\\gamma$. Therefore, the deflated Q-VI admits a potentially sharper convergence-rate characterization than the ambient-space $\\gamma$-bo","title":"Switching-Geometry Analysis of Deflated Q-Value Iteration","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-12T04:43:42Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.10811"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:6b22d7da7645298462decf80cf526b93ed90a0ff0945d37fd1cc6366ccc33888aa1e9ab8fc227e7cfb3cf03a9ef715ef6984c19353b0c9e92395680d55403904","signer":"crovia.substrate","subject":{"observed_at":"2026-05-12T04:43:42Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.10811"},"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":"4d119627aa704f66846905a68039085726a9692b93e584cdeb60464978a430a5","leaf_index":128922,"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":"12ba9901822eef8deeca9aa15669b13bbc7d5376b27ca95362fcf87250828d7a","side":"right"},{"sibling":"43b9f458968b3e13e728a0aca4285c5e28babf61698c23995ce010df27f58481","side":"left"},{"sibling":"8d1f785e5080bdb2b7685652c2a6e7e1d09924048117f7e4ba5d98e47afedf7a","side":"right"},{"sibling":"01f91a334bef688f41ac4d0d7c876304639646d4c9b097c11deae55fad47f28e","side":"left"},{"sibling":"30362f14633d8b9ba995dc1df5a4dfc1b1d7152de324d35d01c2dbd2dfc58350","side":"left"},{"sibling":"bca4ae7c2ec561b665545a6f2f3e419a53afed4a27b8209574392a7c1cbc9439","side":"right"},{"sibling":"c76bba0c216c73590d44e9b2dbdda205cb4803404f532bfebb832fe2ca20fafe","side":"right"},{"sibling":"5eb042446399e2602ae7dd8d9f9f2cac58abf22ff48527ae02c589594da10510","side":"left"},{"sibling":"9b7895252355a8c8a373671590682bbf4d36d41befce49b5e889eaf896415156","side":"left"},{"sibling":"1d74b0fb79eace68949b4d82b0e430b1d9eb122c125f67f5be7d50c074c228e7","side":"left"},{"sibling":"c6eaf7a4fcab2db96e9e9423acb6922c80f64882d0f3f50d09e53a4807d23084","side":"left"},{"sibling":"df12eaabc0a370aff5d0488478f48d2b3f90d025c903643f98ea804b017688ec","side":"right"},{"sibling":"ffc4d51379293bc3e1910c7d612f409dc610fd9acf8241793fb89f82e1bad4ef","side":"left"},{"sibling":"62ac6554017807bd83187f5a3e5f4f72d6c482616429c2780e9fff1f4845fa04","side":"left"},{"sibling":"3a5e69cf0803f4c91f3895ed7c9a95748fef240bec4422e167c05300f79f06c0","side":"left"},{"sibling":"f2817ab288b5324fe49770372c7a10f33f7cd11005f8d4c0a730316f5229dc98","side":"left"},{"sibling":"725fac972e772ca0dc598810ea1abc70df472f72d2d6ab8a0baee2b80e5d2f4c","side":"left"},{"sibling":"98fc57dfef8873b512edc8340f7181df57302bb96777625e072235c62d7c5895","side":"right"}]},"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":134292,"merkle_root":"77fc9c28fae777b81da5b495b3115474df6592dfac590333213d3bdf8b94a9b3","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260515T023701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-15T02:37:25Z","sig_algorithm":"ed25519","signature":"68107a834b00b24f5d4501e5ec727445311f132a486567ecc4c72a4e6dff24c8c21f2de3105293353ba5fdbe370d032819af6aa70f694e2e39b6af6737507009","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_fd9d55f8f8e1a059ea26b4c9d4d3666fe95c38b04cf46211293079733727fe2c"}}