{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:RVLGJWWUZKDMEA5MDOTBQNIKV3","short_pith_number":"pith:RVLGJWWU","schema_version":"1.0","canonical_sha256":"8d5664dad4ca86c203ac1ba618350aaeeb2ef42f2fd98e99541581280cd5faa1","source":{"kind":"arxiv","id":"1807.00255","version":1},"attestation_state":"computed","paper":{"title":"Stochastic model-based minimization under high-order growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Damek Davis, Dmitriy Drusvyatskiy, Kellie J. MacPhee","submitted_at":"2018-07-01T01:49:22Z","abstract_excerpt":"Given a nonsmooth, nonconvex minimization problem, we consider algorithms that iteratively sample and minimize stochastic convex models of the objective function. Assuming that the one-sided approximation quality and the variation of the models is controlled by a Bregman divergence, we show that the scheme drives a natural stationarity measure to zero at the rate $O(k^{-1/4})$. Under additional convexity and relative strong convexity assumptions, the function values converge to the minimum at the rate of $O(k^{-1/2})$ and $\\widetilde{O}(k^{-1})$, respectively. We discuss consequences for stoch"},"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":"1807.00255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-01T01:49:22Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"0a857e14652c7041776c51f683083aeb2e3a6f61f42636a6a767926328ed3e5c","abstract_canon_sha256":"99267b4dcd1cef52c98ae7353fd97bbd4931dc638905109ee39d7881071ed2dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:55.531463Z","signature_b64":"jqUUqF/rcswIJQTpmNwtYBH2TsJmIRpFrcKH+ZJqg0lkg/NjuqaU2a2ICKNpWxktzLzfaR8c97JqQhVwG9b0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d5664dad4ca86c203ac1ba618350aaeeb2ef42f2fd98e99541581280cd5faa1","last_reissued_at":"2026-05-18T00:11:55.530949Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:55.530949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic model-based minimization under high-order growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Damek Davis, Dmitriy Drusvyatskiy, Kellie J. MacPhee","submitted_at":"2018-07-01T01:49:22Z","abstract_excerpt":"Given a nonsmooth, nonconvex minimization problem, we consider algorithms that iteratively sample and minimize stochastic convex models of the objective function. Assuming that the one-sided approximation quality and the variation of the models is controlled by a Bregman divergence, we show that the scheme drives a natural stationarity measure to zero at the rate $O(k^{-1/4})$. Under additional convexity and relative strong convexity assumptions, the function values converge to the minimum at the rate of $O(k^{-1/2})$ and $\\widetilde{O}(k^{-1})$, respectively. We discuss consequences for stoch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00255","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":""},"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":"1807.00255","created_at":"2026-05-18T00:11:55.531029+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.00255v1","created_at":"2026-05-18T00:11:55.531029+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00255","created_at":"2026-05-18T00:11:55.531029+00:00"},{"alias_kind":"pith_short_12","alias_value":"RVLGJWWUZKDM","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"RVLGJWWUZKDMEA5M","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"RVLGJWWU","created_at":"2026-05-18T12:32:50.500415+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RVLGJWWUZKDMEA5MDOTBQNIKV3","json":"https://pith.science/pith/RVLGJWWUZKDMEA5MDOTBQNIKV3.json","graph_json":"https://pith.science/api/pith-number/RVLGJWWUZKDMEA5MDOTBQNIKV3/graph.json","events_json":"https://pith.science/api/pith-number/RVLGJWWUZKDMEA5MDOTBQNIKV3/events.json","paper":"https://pith.science/paper/RVLGJWWU"},"agent_actions":{"view_html":"https://pith.science/pith/RVLGJWWUZKDMEA5MDOTBQNIKV3","download_json":"https://pith.science/pith/RVLGJWWUZKDMEA5MDOTBQNIKV3.json","view_paper":"https://pith.science/paper/RVLGJWWU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.00255&json=true","fetch_graph":"https://pith.science/api/pith-number/RVLGJWWUZKDMEA5MDOTBQNIKV3/graph.json","fetch_events":"https://pith.science/api/pith-number/RVLGJWWUZKDMEA5MDOTBQNIKV3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RVLGJWWUZKDMEA5MDOTBQNIKV3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RVLGJWWUZKDMEA5MDOTBQNIKV3/action/storage_attestation","attest_author":"https://pith.science/pith/RVLGJWWUZKDMEA5MDOTBQNIKV3/action/author_attestation","sign_citation":"https://pith.science/pith/RVLGJWWUZKDMEA5MDOTBQNIKV3/action/citation_signature","submit_replication":"https://pith.science/pith/RVLGJWWUZKDMEA5MDOTBQNIKV3/action/replication_record"}},"created_at":"2026-05-18T00:11:55.531029+00:00","updated_at":"2026-05-18T00:11:55.531029+00:00"}