{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:K7PPXIPGS4N5IRL5LMQNTETT3E","short_pith_number":"pith:K7PPXIPG","schema_version":"1.0","canonical_sha256":"57defba1e6971bd4457d5b20d99273d92b0c67e72c47498e3a234b940bb833f9","source":{"kind":"arxiv","id":"2412.17070","version":5},"attestation_state":"computed","paper":{"title":"Decoupled Functional Central Limit Theorems for Two-Time-Scale Stochastic Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"math.PR","authors_text":"Jiadong Liang, Xiang Li, Yuze Han, Zhihua Zhang","submitted_at":"2024-12-22T15:43:01Z","abstract_excerpt":"In two-time-scale stochastic approximation (SA), two iterates are updated at different rates, governed by distinct step sizes, with each update influencing the other. Previous studies have demonstrated that the convergence rates of the error terms for these updates depend solely on their respective step sizes, a property known as decoupled convergence. However, a functional version of this decoupled convergence has not been explored. Our work fills this gap by establishing decoupled functional central limit theorems for two-time-scale SA, offering a more precise characterization of its asympto"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2412.17070","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-22T15:43:01Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"0d44cc48508e5d858c32b92478ffef1ceff85de03a5bdbfc1da90118772bc183","abstract_canon_sha256":"2c1ba84e6e9a52a81d7ea8c1f66e95d0d7767c2b9b2958bab3fa2451737876c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:16:49.566229Z","signature_b64":"62xQBfuJ612+1jMRgECaeyUsg10u8hzn3LLwm+Wd0r16+V2PBXACl7uizYaaCl0Omkq8o1pWfvva0bFqlPEHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57defba1e6971bd4457d5b20d99273d92b0c67e72c47498e3a234b940bb833f9","last_reissued_at":"2026-06-30T02:16:49.565542Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:16:49.565542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decoupled Functional Central Limit Theorems for Two-Time-Scale Stochastic Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"math.PR","authors_text":"Jiadong Liang, Xiang Li, Yuze Han, Zhihua Zhang","submitted_at":"2024-12-22T15:43:01Z","abstract_excerpt":"In two-time-scale stochastic approximation (SA), two iterates are updated at different rates, governed by distinct step sizes, with each update influencing the other. Previous studies have demonstrated that the convergence rates of the error terms for these updates depend solely on their respective step sizes, a property known as decoupled convergence. However, a functional version of this decoupled convergence has not been explored. Our work fills this gap by establishing decoupled functional central limit theorems for two-time-scale SA, offering a more precise characterization of its asympto"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.17070","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.17070/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2412.17070","created_at":"2026-06-30T02:16:49.565630+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.17070v5","created_at":"2026-06-30T02:16:49.565630+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.17070","created_at":"2026-06-30T02:16:49.565630+00:00"},{"alias_kind":"pith_short_12","alias_value":"K7PPXIPGS4N5","created_at":"2026-06-30T02:16:49.565630+00:00"},{"alias_kind":"pith_short_16","alias_value":"K7PPXIPGS4N5IRL5","created_at":"2026-06-30T02:16:49.565630+00:00"},{"alias_kind":"pith_short_8","alias_value":"K7PPXIPG","created_at":"2026-06-30T02:16:49.565630+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.18964","citing_title":"Central Limit Theorems for Asynchronous Averaged Q-Learning","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/K7PPXIPGS4N5IRL5LMQNTETT3E","json":"https://pith.science/pith/K7PPXIPGS4N5IRL5LMQNTETT3E.json","graph_json":"https://pith.science/api/pith-number/K7PPXIPGS4N5IRL5LMQNTETT3E/graph.json","events_json":"https://pith.science/api/pith-number/K7PPXIPGS4N5IRL5LMQNTETT3E/events.json","paper":"https://pith.science/paper/K7PPXIPG"},"agent_actions":{"view_html":"https://pith.science/pith/K7PPXIPGS4N5IRL5LMQNTETT3E","download_json":"https://pith.science/pith/K7PPXIPGS4N5IRL5LMQNTETT3E.json","view_paper":"https://pith.science/paper/K7PPXIPG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.17070&json=true","fetch_graph":"https://pith.science/api/pith-number/K7PPXIPGS4N5IRL5LMQNTETT3E/graph.json","fetch_events":"https://pith.science/api/pith-number/K7PPXIPGS4N5IRL5LMQNTETT3E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K7PPXIPGS4N5IRL5LMQNTETT3E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K7PPXIPGS4N5IRL5LMQNTETT3E/action/storage_attestation","attest_author":"https://pith.science/pith/K7PPXIPGS4N5IRL5LMQNTETT3E/action/author_attestation","sign_citation":"https://pith.science/pith/K7PPXIPGS4N5IRL5LMQNTETT3E/action/citation_signature","submit_replication":"https://pith.science/pith/K7PPXIPGS4N5IRL5LMQNTETT3E/action/replication_record"}},"created_at":"2026-06-30T02:16:49.565630+00:00","updated_at":"2026-06-30T02:16:49.565630+00:00"}