{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:DLCSL7NBBNFCIYCTXME2EOVXHX","short_pith_number":"pith:DLCSL7NB","schema_version":"1.0","canonical_sha256":"1ac525fda10b4a246053bb09a23ab73dd646554214031efd969383c393e06c1c","source":{"kind":"arxiv","id":"1307.7192","version":1},"attestation_state":"computed","paper":{"title":"MixedGrad: An O(1/T) Convergence Rate Algorithm for Stochastic Smooth Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Mehrdad Mahdavi, Rong Jin","submitted_at":"2013-07-26T23:27:23Z","abstract_excerpt":"It is well known that the optimal convergence rate for stochastic optimization of smooth functions is $O(1/\\sqrt{T})$, which is same as stochastic optimization of Lipschitz continuous convex functions. This is in contrast to optimizing smooth functions using full gradients, which yields a convergence rate of $O(1/T^2)$. In this work, we consider a new setup for optimizing smooth functions, termed as {\\bf Mixed Optimization}, which allows to access both a stochastic oracle and a full gradient oracle. Our goal is to significantly improve the convergence rate of stochastic optimization of smooth "},"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":"1307.7192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-07-26T23:27:23Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"b6ef456164aa9b838149182ccbb9957125f72c9012ea2ec94dcac9ca4e1c2845","abstract_canon_sha256":"4a4ac4df65f918d8966287ac447461c6ba3a8414984c713d65e3ce0a2fcd1f72"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:23.964163Z","signature_b64":"vCJtY2YrH7VOGYW2BOU5/9o2DvSzZGiFrfcOHkpPzcbeWExks8uG3QTPSIj/T01FlF2BJqYN20OcHwDSPxE9Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ac525fda10b4a246053bb09a23ab73dd646554214031efd969383c393e06c1c","last_reissued_at":"2026-05-18T03:17:23.963507Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:23.963507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"MixedGrad: An O(1/T) Convergence Rate Algorithm for Stochastic Smooth Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Mehrdad Mahdavi, Rong Jin","submitted_at":"2013-07-26T23:27:23Z","abstract_excerpt":"It is well known that the optimal convergence rate for stochastic optimization of smooth functions is $O(1/\\sqrt{T})$, which is same as stochastic optimization of Lipschitz continuous convex functions. This is in contrast to optimizing smooth functions using full gradients, which yields a convergence rate of $O(1/T^2)$. In this work, we consider a new setup for optimizing smooth functions, termed as {\\bf Mixed Optimization}, which allows to access both a stochastic oracle and a full gradient oracle. Our goal is to significantly improve the convergence rate of stochastic optimization of smooth "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7192","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":"1307.7192","created_at":"2026-05-18T03:17:23.963606+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.7192v1","created_at":"2026-05-18T03:17:23.963606+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7192","created_at":"2026-05-18T03:17:23.963606+00:00"},{"alias_kind":"pith_short_12","alias_value":"DLCSL7NBBNFC","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"DLCSL7NBBNFCIYCT","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"DLCSL7NB","created_at":"2026-05-18T12:27:43.054852+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/DLCSL7NBBNFCIYCTXME2EOVXHX","json":"https://pith.science/pith/DLCSL7NBBNFCIYCTXME2EOVXHX.json","graph_json":"https://pith.science/api/pith-number/DLCSL7NBBNFCIYCTXME2EOVXHX/graph.json","events_json":"https://pith.science/api/pith-number/DLCSL7NBBNFCIYCTXME2EOVXHX/events.json","paper":"https://pith.science/paper/DLCSL7NB"},"agent_actions":{"view_html":"https://pith.science/pith/DLCSL7NBBNFCIYCTXME2EOVXHX","download_json":"https://pith.science/pith/DLCSL7NBBNFCIYCTXME2EOVXHX.json","view_paper":"https://pith.science/paper/DLCSL7NB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.7192&json=true","fetch_graph":"https://pith.science/api/pith-number/DLCSL7NBBNFCIYCTXME2EOVXHX/graph.json","fetch_events":"https://pith.science/api/pith-number/DLCSL7NBBNFCIYCTXME2EOVXHX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DLCSL7NBBNFCIYCTXME2EOVXHX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DLCSL7NBBNFCIYCTXME2EOVXHX/action/storage_attestation","attest_author":"https://pith.science/pith/DLCSL7NBBNFCIYCTXME2EOVXHX/action/author_attestation","sign_citation":"https://pith.science/pith/DLCSL7NBBNFCIYCTXME2EOVXHX/action/citation_signature","submit_replication":"https://pith.science/pith/DLCSL7NBBNFCIYCTXME2EOVXHX/action/replication_record"}},"created_at":"2026-05-18T03:17:23.963606+00:00","updated_at":"2026-05-18T03:17:23.963606+00:00"}