{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:5GMP2QSGDBLDRUALNGK6ZGOJQA","short_pith_number":"pith:5GMP2QSG","schema_version":"1.0","canonical_sha256":"e998fd4246185638d00b6995ec99c9801ecd5c116bb29dc1bc27acb2131ba1cb","source":{"kind":"arxiv","id":"2501.08256","version":1},"attestation_state":"computed","paper":{"title":"Convergence of projected stochastic approximation algorithm","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"B{\\l}a\\.zej Miasojedow, Micha{\\l} Borowski","submitted_at":"2025-01-14T17:04:20Z","abstract_excerpt":"We study the Robbins-Monro stochastic approximation algorithm with projections on a hyperrectangle and prove its convergence. This work fills a gap in the convergence proof of the classic book by Kushner and Yin. Using the ODE method, we show that the algorithm converges to stationary points of a related projected ODE. Our results provide a better theoretical foundation for stochastic optimization techniques, including stochastic gradient descent and its proximal version. These results extend the algorithm's applicability and relax some assumptions of previous research."},"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":"2501.08256","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-01-14T17:04:20Z","cross_cats_sorted":[],"title_canon_sha256":"0c7d51d48f1c9e58a37fba8a50dc18fa05eeb10edb08852eebaa290304920d2d","abstract_canon_sha256":"391d4a9d1200e64e85dee03f86218901a3fa5ed448891e916a87c2a096b0e089"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:00:58.541705Z","signature_b64":"21O9Lj82//beumuyUJm3GrAA0eXO6zIZWz1x8OUjeU123QorF20jpsp0uJ5mKyyi371g9Uv4S3SjddPHwdW6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e998fd4246185638d00b6995ec99c9801ecd5c116bb29dc1bc27acb2131ba1cb","last_reissued_at":"2026-07-05T10:00:58.541252Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:00:58.541252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence of projected stochastic approximation algorithm","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"B{\\l}a\\.zej Miasojedow, Micha{\\l} Borowski","submitted_at":"2025-01-14T17:04:20Z","abstract_excerpt":"We study the Robbins-Monro stochastic approximation algorithm with projections on a hyperrectangle and prove its convergence. This work fills a gap in the convergence proof of the classic book by Kushner and Yin. Using the ODE method, we show that the algorithm converges to stationary points of a related projected ODE. Our results provide a better theoretical foundation for stochastic optimization techniques, including stochastic gradient descent and its proximal version. These results extend the algorithm's applicability and relax some assumptions of previous research."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.08256","kind":"arxiv","version":1},"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/2501.08256/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":"2501.08256","created_at":"2026-07-05T10:00:58.541308+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.08256v1","created_at":"2026-07-05T10:00:58.541308+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.08256","created_at":"2026-07-05T10:00:58.541308+00:00"},{"alias_kind":"pith_short_12","alias_value":"5GMP2QSGDBLD","created_at":"2026-07-05T10:00:58.541308+00:00"},{"alias_kind":"pith_short_16","alias_value":"5GMP2QSGDBLDRUAL","created_at":"2026-07-05T10:00:58.541308+00:00"},{"alias_kind":"pith_short_8","alias_value":"5GMP2QSG","created_at":"2026-07-05T10:00:58.541308+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.26901","citing_title":"Load Management of Distribution Systems via Online Dynamic Pricing","ref_index":47,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5GMP2QSGDBLDRUALNGK6ZGOJQA","json":"https://pith.science/pith/5GMP2QSGDBLDRUALNGK6ZGOJQA.json","graph_json":"https://pith.science/api/pith-number/5GMP2QSGDBLDRUALNGK6ZGOJQA/graph.json","events_json":"https://pith.science/api/pith-number/5GMP2QSGDBLDRUALNGK6ZGOJQA/events.json","paper":"https://pith.science/paper/5GMP2QSG"},"agent_actions":{"view_html":"https://pith.science/pith/5GMP2QSGDBLDRUALNGK6ZGOJQA","download_json":"https://pith.science/pith/5GMP2QSGDBLDRUALNGK6ZGOJQA.json","view_paper":"https://pith.science/paper/5GMP2QSG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.08256&json=true","fetch_graph":"https://pith.science/api/pith-number/5GMP2QSGDBLDRUALNGK6ZGOJQA/graph.json","fetch_events":"https://pith.science/api/pith-number/5GMP2QSGDBLDRUALNGK6ZGOJQA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5GMP2QSGDBLDRUALNGK6ZGOJQA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5GMP2QSGDBLDRUALNGK6ZGOJQA/action/storage_attestation","attest_author":"https://pith.science/pith/5GMP2QSGDBLDRUALNGK6ZGOJQA/action/author_attestation","sign_citation":"https://pith.science/pith/5GMP2QSGDBLDRUALNGK6ZGOJQA/action/citation_signature","submit_replication":"https://pith.science/pith/5GMP2QSGDBLDRUALNGK6ZGOJQA/action/replication_record"}},"created_at":"2026-07-05T10:00:58.541308+00:00","updated_at":"2026-07-05T10:00:58.541308+00:00"}