{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:I53UEPPGLSDACEFSNP36USASWU","short_pith_number":"pith:I53UEPPG","canonical_record":{"source":{"id":"2001.07819","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2020-01-22T00:05:14Z","cross_cats_sorted":["cs.DS","cs.LG","math.OC"],"title_canon_sha256":"7d0852e4e952cd64e11fb70bbca496a5594ab6a26b5680366947a268aee6c212","abstract_canon_sha256":"d86540f8f2627f4204b388d99652ba9b0cea2ffdbf76f1ffc3a630965e521eb1"},"schema_version":"1.0"},"canonical_sha256":"4777423de65c860110b26bf7ea4812b51597d9925a62a1b4a713704599d04403","source":{"kind":"arxiv","id":"2001.07819","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.07819","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"2001.07819v2","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.07819","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"I53UEPPGLSDA","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"pith_short_16","alias_value":"I53UEPPGLSDACEFS","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"pith_short_8","alias_value":"I53UEPPG","created_at":"2026-07-05T04:11:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:I53UEPPGLSDACEFSNP36USASWU","target":"record","payload":{"canonical_record":{"source":{"id":"2001.07819","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2020-01-22T00:05:14Z","cross_cats_sorted":["cs.DS","cs.LG","math.OC"],"title_canon_sha256":"7d0852e4e952cd64e11fb70bbca496a5594ab6a26b5680366947a268aee6c212","abstract_canon_sha256":"d86540f8f2627f4204b388d99652ba9b0cea2ffdbf76f1ffc3a630965e521eb1"},"schema_version":"1.0"},"canonical_sha256":"4777423de65c860110b26bf7ea4812b51597d9925a62a1b4a713704599d04403","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:11:22.534480Z","signature_b64":"R9R+XxliCXNck90zzQtAdOlMbUVh1kSmhX922NH955FzkV8zaEyC1fCXkO1S7yqeJ/c4tYny4OcEni4NcbQrAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4777423de65c860110b26bf7ea4812b51597d9925a62a1b4a713704599d04403","last_reissued_at":"2026-07-05T04:11:22.533923Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:11:22.533923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2001.07819","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:11:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HH87kOBemh/dsQJf3I9m5zEI3kyp77/9NAfXUGxL1M5GwpT37WqPOKiY1jRiTE8X26axdqtwABmi0YkcqP2wBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T06:24:44.067556Z"},"content_sha256":"4140b7648ae8e4849319f87b07db691b2d38c7a428e5e9c049e327b84aabfc6c","schema_version":"1.0","event_id":"sha256:4140b7648ae8e4849319f87b07db691b2d38c7a428e5e9c049e327b84aabfc6c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:I53UEPPGLSDACEFSNP36USASWU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zeroth-Order Algorithms for Nonconvex Minimax Problems with Improved Complexities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS","cs.LG","math.OC"],"primary_cat":"stat.ML","authors_text":"Krishnakumar Balasubramanian, Meisam Razaviyayn, Shiqian Ma, Zhongruo Wang","submitted_at":"2020-01-22T00:05:14Z","abstract_excerpt":"In this paper, we study zeroth-order algorithms for minimax optimization problems that are nonconvex in one variable and strongly-concave in the other variable. Such minimax optimization problems have attracted significant attention lately due to their applications in modern machine learning tasks. We first consider a deterministic version of the problem. We design and analyze the Zeroth-Order Gradient Descent Ascent (\\texttt{ZO-GDA}) algorithm, and provide improved results compared to existing works, in terms of oracle complexity. We also propose the Zeroth-Order Gradient Descent Multi-Step A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.07819","kind":"arxiv","version":2},"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/2001.07819/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:11:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hgq9vQQBsIkXSjntpFqc+OwouWzrS4G31qTTspM8QWNgX09BBR2paYvmzcdCcdPrFAeRuecSodZXICTiDyh2Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T06:24:44.068127Z"},"content_sha256":"684193e3630caabcb5a45077ad544dc7b3eec67c44543ea643647ffc3a7938e4","schema_version":"1.0","event_id":"sha256:684193e3630caabcb5a45077ad544dc7b3eec67c44543ea643647ffc3a7938e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I53UEPPGLSDACEFSNP36USASWU/bundle.json","state_url":"https://pith.science/pith/I53UEPPGLSDACEFSNP36USASWU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I53UEPPGLSDACEFSNP36USASWU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-14T06:24:44Z","links":{"resolver":"https://pith.science/pith/I53UEPPGLSDACEFSNP36USASWU","bundle":"https://pith.science/pith/I53UEPPGLSDACEFSNP36USASWU/bundle.json","state":"https://pith.science/pith/I53UEPPGLSDACEFSNP36USASWU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I53UEPPGLSDACEFSNP36USASWU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:I53UEPPGLSDACEFSNP36USASWU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d86540f8f2627f4204b388d99652ba9b0cea2ffdbf76f1ffc3a630965e521eb1","cross_cats_sorted":["cs.DS","cs.LG","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2020-01-22T00:05:14Z","title_canon_sha256":"7d0852e4e952cd64e11fb70bbca496a5594ab6a26b5680366947a268aee6c212"},"schema_version":"1.0","source":{"id":"2001.07819","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.07819","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"2001.07819v2","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.07819","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"I53UEPPGLSDA","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"pith_short_16","alias_value":"I53UEPPGLSDACEFS","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"pith_short_8","alias_value":"I53UEPPG","created_at":"2026-07-05T04:11:22Z"}],"graph_snapshots":[{"event_id":"sha256:684193e3630caabcb5a45077ad544dc7b3eec67c44543ea643647ffc3a7938e4","target":"graph","created_at":"2026-07-05T04:11:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2001.07819/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study zeroth-order algorithms for minimax optimization problems that are nonconvex in one variable and strongly-concave in the other variable. Such minimax optimization problems have attracted significant attention lately due to their applications in modern machine learning tasks. We first consider a deterministic version of the problem. We design and analyze the Zeroth-Order Gradient Descent Ascent (\\texttt{ZO-GDA}) algorithm, and provide improved results compared to existing works, in terms of oracle complexity. We also propose the Zeroth-Order Gradient Descent Multi-Step A","authors_text":"Krishnakumar Balasubramanian, Meisam Razaviyayn, Shiqian Ma, Zhongruo Wang","cross_cats":["cs.DS","cs.LG","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2020-01-22T00:05:14Z","title":"Zeroth-Order Algorithms for Nonconvex Minimax Problems with Improved Complexities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.07819","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4140b7648ae8e4849319f87b07db691b2d38c7a428e5e9c049e327b84aabfc6c","target":"record","created_at":"2026-07-05T04:11:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d86540f8f2627f4204b388d99652ba9b0cea2ffdbf76f1ffc3a630965e521eb1","cross_cats_sorted":["cs.DS","cs.LG","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2020-01-22T00:05:14Z","title_canon_sha256":"7d0852e4e952cd64e11fb70bbca496a5594ab6a26b5680366947a268aee6c212"},"schema_version":"1.0","source":{"id":"2001.07819","kind":"arxiv","version":2}},"canonical_sha256":"4777423de65c860110b26bf7ea4812b51597d9925a62a1b4a713704599d04403","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4777423de65c860110b26bf7ea4812b51597d9925a62a1b4a713704599d04403","first_computed_at":"2026-07-05T04:11:22.533923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:11:22.533923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R9R+XxliCXNck90zzQtAdOlMbUVh1kSmhX922NH955FzkV8zaEyC1fCXkO1S7yqeJ/c4tYny4OcEni4NcbQrAw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:11:22.534480Z","signed_message":"canonical_sha256_bytes"},"source_id":"2001.07819","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4140b7648ae8e4849319f87b07db691b2d38c7a428e5e9c049e327b84aabfc6c","sha256:684193e3630caabcb5a45077ad544dc7b3eec67c44543ea643647ffc3a7938e4"],"state_sha256":"1b310e94b0d69c717c2d7baa6df42e232dd77e254f00a0dc4431241f53f2d56a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U5LQ+crp5wIlX/zs/B/eM5vIbBBEaM1D82NIW/Us+hqkFf91Z1AsP5ECLYJj3GtaA3ZJnKlI/d0ufg7FQ28ABQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T06:24:44.072902Z","bundle_sha256":"6c86b3ba17538cef0cb35a4ed9d195b84a4e1ec63a05e881b35cb8e5aa0e4f38"}}