{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:XPY3UBV2N75HQNMQ3PNYU3C36E","short_pith_number":"pith:XPY3UBV2","schema_version":"1.0","canonical_sha256":"bbf1ba06ba6ffa783590dbdb8a6c5bf126942950cb37d1e12485d7a393f795c2","source":{"kind":"arxiv","id":"2408.11974","version":3},"attestation_state":"computed","paper":{"title":"Two-Timescale Gradient Descent Ascent Algorithms for Nonconvex Minimax Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Chi Jin, Michael. I. Jordan, Tianyi Lin","submitted_at":"2024-08-21T20:14:54Z","abstract_excerpt":"We provide a unified analysis of two-timescale gradient descent ascent (TTGDA) for solving structured nonconvex minimax optimization problems in the form of $\\min_\\textbf{x} \\max_{\\textbf{y} \\in Y} f(\\textbf{x}, \\textbf{y})$, where the objective function $f(\\textbf{x}, \\textbf{y})$ is nonconvex in $\\textbf{x}$ and concave in $\\textbf{y}$, and the constraint set $Y \\subseteq \\mathbb{R}^n$ is convex and bounded. In the convex-concave setting, the single-timescale gradient descent ascent (GDA) algorithm is widely used in applications and has been shown to have strong convergence guarantees. In mo"},"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":"2408.11974","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-08-21T20:14:54Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"000f7c1699f09bb05fb57891bf857bcc086e69147042d210334da6a348c5cad3","abstract_canon_sha256":"7ddabe30605f7752e7a755d6cb2ea05a6770e49f82bc7ed550ef7c457257b126"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:05:44.507614Z","signature_b64":"qDkNmIAWO4UT4L2lkVUawLbTVEu/hG+IWc/7e8ANRQbtqKDCjJskDI5w9dwjnbcN+uA4J1XPMWUvnfbsYqHgDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbf1ba06ba6ffa783590dbdb8a6c5bf126942950cb37d1e12485d7a393f795c2","last_reissued_at":"2026-07-05T10:05:44.507109Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:05:44.507109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two-Timescale Gradient Descent Ascent Algorithms for Nonconvex Minimax Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Chi Jin, Michael. I. Jordan, Tianyi Lin","submitted_at":"2024-08-21T20:14:54Z","abstract_excerpt":"We provide a unified analysis of two-timescale gradient descent ascent (TTGDA) for solving structured nonconvex minimax optimization problems in the form of $\\min_\\textbf{x} \\max_{\\textbf{y} \\in Y} f(\\textbf{x}, \\textbf{y})$, where the objective function $f(\\textbf{x}, \\textbf{y})$ is nonconvex in $\\textbf{x}$ and concave in $\\textbf{y}$, and the constraint set $Y \\subseteq \\mathbb{R}^n$ is convex and bounded. In the convex-concave setting, the single-timescale gradient descent ascent (GDA) algorithm is widely used in applications and has been shown to have strong convergence guarantees. In mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.11974","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/2408.11974/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":"2408.11974","created_at":"2026-07-05T10:05:44.507169+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.11974v3","created_at":"2026-07-05T10:05:44.507169+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.11974","created_at":"2026-07-05T10:05:44.507169+00:00"},{"alias_kind":"pith_short_12","alias_value":"XPY3UBV2N75H","created_at":"2026-07-05T10:05:44.507169+00:00"},{"alias_kind":"pith_short_16","alias_value":"XPY3UBV2N75HQNMQ","created_at":"2026-07-05T10:05:44.507169+00:00"},{"alias_kind":"pith_short_8","alias_value":"XPY3UBV2","created_at":"2026-07-05T10:05:44.507169+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2501.10806","citing_title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","ref_index":20,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XPY3UBV2N75HQNMQ3PNYU3C36E","json":"https://pith.science/pith/XPY3UBV2N75HQNMQ3PNYU3C36E.json","graph_json":"https://pith.science/api/pith-number/XPY3UBV2N75HQNMQ3PNYU3C36E/graph.json","events_json":"https://pith.science/api/pith-number/XPY3UBV2N75HQNMQ3PNYU3C36E/events.json","paper":"https://pith.science/paper/XPY3UBV2"},"agent_actions":{"view_html":"https://pith.science/pith/XPY3UBV2N75HQNMQ3PNYU3C36E","download_json":"https://pith.science/pith/XPY3UBV2N75HQNMQ3PNYU3C36E.json","view_paper":"https://pith.science/paper/XPY3UBV2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.11974&json=true","fetch_graph":"https://pith.science/api/pith-number/XPY3UBV2N75HQNMQ3PNYU3C36E/graph.json","fetch_events":"https://pith.science/api/pith-number/XPY3UBV2N75HQNMQ3PNYU3C36E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XPY3UBV2N75HQNMQ3PNYU3C36E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XPY3UBV2N75HQNMQ3PNYU3C36E/action/storage_attestation","attest_author":"https://pith.science/pith/XPY3UBV2N75HQNMQ3PNYU3C36E/action/author_attestation","sign_citation":"https://pith.science/pith/XPY3UBV2N75HQNMQ3PNYU3C36E/action/citation_signature","submit_replication":"https://pith.science/pith/XPY3UBV2N75HQNMQ3PNYU3C36E/action/replication_record"}},"created_at":"2026-07-05T10:05:44.507169+00:00","updated_at":"2026-07-05T10:05:44.507169+00:00"}