{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:JCNOAPEMJAZDTLOK3O6XCGE623","short_pith_number":"pith:JCNOAPEM","schema_version":"1.0","canonical_sha256":"489ae03c8c483239adcadbbd71189ed6ce98a58e821997609526d397f4b71977","source":{"kind":"arxiv","id":"1906.01115","version":3},"attestation_state":"computed","paper":{"title":"Convergence Rate of $\\mathcal{O}(1/k)$ for Optimistic Gradient and Extra-gradient Methods in Smooth Convex-Concave Saddle Point Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Aryan Mokhtari, Asuman Ozdaglar, Sarath Pattathil","submitted_at":"2019-06-03T22:54:41Z","abstract_excerpt":"We study the iteration complexity of the optimistic gradient descent-ascent (OGDA) method and the extra-gradient (EG) method for finding a saddle point of a convex-concave unconstrained min-max problem. To do so, we first show that both OGDA and EG can be interpreted as approximate variants of the proximal point method. This is similar to the approach taken in [Nemirovski, 2004] which analyzes EG as an approximation of the `conceptual mirror prox'. In this paper, we highlight how gradients used in OGDA and EG try to approximate the gradient of the Proximal Point method. We then exploit this in"},"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":"1906.01115","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-03T22:54:41Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"ce07098ac14832f05cffdd656ff70f4e584d1e530bdbd3a3e92ccadb6e18145c","abstract_canon_sha256":"8b3394da35be08b6b7669b1878f9981b2a2ce31de80d9db815368fbc101bc384"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:38:32.889643Z","signature_b64":"GLxqHRC4roplTc5PoszS9qY4UnsY5VbFlaJhn/xz3qe8aMDsg4/lf47CI8VhiF75HI03cH5S29Fp8Mmr+76BCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"489ae03c8c483239adcadbbd71189ed6ce98a58e821997609526d397f4b71977","last_reissued_at":"2026-07-05T01:38:32.889181Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:38:32.889181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence Rate of $\\mathcal{O}(1/k)$ for Optimistic Gradient and Extra-gradient Methods in Smooth Convex-Concave Saddle Point Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Aryan Mokhtari, Asuman Ozdaglar, Sarath Pattathil","submitted_at":"2019-06-03T22:54:41Z","abstract_excerpt":"We study the iteration complexity of the optimistic gradient descent-ascent (OGDA) method and the extra-gradient (EG) method for finding a saddle point of a convex-concave unconstrained min-max problem. To do so, we first show that both OGDA and EG can be interpreted as approximate variants of the proximal point method. This is similar to the approach taken in [Nemirovski, 2004] which analyzes EG as an approximation of the `conceptual mirror prox'. In this paper, we highlight how gradients used in OGDA and EG try to approximate the gradient of the Proximal Point method. We then exploit this in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01115","kind":"arxiv","version":3},"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/1906.01115/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":"1906.01115","created_at":"2026-07-05T01:38:32.889250+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.01115v3","created_at":"2026-07-05T01:38:32.889250+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01115","created_at":"2026-07-05T01:38:32.889250+00:00"},{"alias_kind":"pith_short_12","alias_value":"JCNOAPEMJAZD","created_at":"2026-07-05T01:38:32.889250+00:00"},{"alias_kind":"pith_short_16","alias_value":"JCNOAPEMJAZDTLOK","created_at":"2026-07-05T01:38:32.889250+00:00"},{"alias_kind":"pith_short_8","alias_value":"JCNOAPEM","created_at":"2026-07-05T01:38:32.889250+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.14371","citing_title":"Layer-wise Quantization for Quantized Optimistic Dual Averaging","ref_index":68,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JCNOAPEMJAZDTLOK3O6XCGE623","json":"https://pith.science/pith/JCNOAPEMJAZDTLOK3O6XCGE623.json","graph_json":"https://pith.science/api/pith-number/JCNOAPEMJAZDTLOK3O6XCGE623/graph.json","events_json":"https://pith.science/api/pith-number/JCNOAPEMJAZDTLOK3O6XCGE623/events.json","paper":"https://pith.science/paper/JCNOAPEM"},"agent_actions":{"view_html":"https://pith.science/pith/JCNOAPEMJAZDTLOK3O6XCGE623","download_json":"https://pith.science/pith/JCNOAPEMJAZDTLOK3O6XCGE623.json","view_paper":"https://pith.science/paper/JCNOAPEM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.01115&json=true","fetch_graph":"https://pith.science/api/pith-number/JCNOAPEMJAZDTLOK3O6XCGE623/graph.json","fetch_events":"https://pith.science/api/pith-number/JCNOAPEMJAZDTLOK3O6XCGE623/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JCNOAPEMJAZDTLOK3O6XCGE623/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JCNOAPEMJAZDTLOK3O6XCGE623/action/storage_attestation","attest_author":"https://pith.science/pith/JCNOAPEMJAZDTLOK3O6XCGE623/action/author_attestation","sign_citation":"https://pith.science/pith/JCNOAPEMJAZDTLOK3O6XCGE623/action/citation_signature","submit_replication":"https://pith.science/pith/JCNOAPEMJAZDTLOK3O6XCGE623/action/replication_record"}},"created_at":"2026-07-05T01:38:32.889250+00:00","updated_at":"2026-07-05T01:38:32.889250+00:00"}