{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:GEKWMJUZ74RQOFYAJYKHWSZKQC","short_pith_number":"pith:GEKWMJUZ","canonical_record":{"source":{"id":"2006.09361","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-06-16T17:55:46Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"b9c7e3a68b0cf3d0ad2d34670a2e48a7a2926834484322ddbccb4dc84c13d844","abstract_canon_sha256":"8d45215df13939f44f35db8f3306e450e4b33a5a858a492223573c8e87b5a62c"},"schema_version":"1.0"},"canonical_sha256":"3115662699ff230717004e147b4b2a80b9f0b462057cf0c7d1bf94bb13b54ab0","source":{"kind":"arxiv","id":"2006.09361","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.09361","created_at":"2026-07-05T02:25:10Z"},{"alias_kind":"arxiv_version","alias_value":"2006.09361v3","created_at":"2026-07-05T02:25:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.09361","created_at":"2026-07-05T02:25:10Z"},{"alias_kind":"pith_short_12","alias_value":"GEKWMJUZ74RQ","created_at":"2026-07-05T02:25:10Z"},{"alias_kind":"pith_short_16","alias_value":"GEKWMJUZ74RQOFYA","created_at":"2026-07-05T02:25:10Z"},{"alias_kind":"pith_short_8","alias_value":"GEKWMJUZ","created_at":"2026-07-05T02:25:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:GEKWMJUZ74RQOFYAJYKHWSZKQC","target":"record","payload":{"canonical_record":{"source":{"id":"2006.09361","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-06-16T17:55:46Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"b9c7e3a68b0cf3d0ad2d34670a2e48a7a2926834484322ddbccb4dc84c13d844","abstract_canon_sha256":"8d45215df13939f44f35db8f3306e450e4b33a5a858a492223573c8e87b5a62c"},"schema_version":"1.0"},"canonical_sha256":"3115662699ff230717004e147b4b2a80b9f0b462057cf0c7d1bf94bb13b54ab0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:25:10.322123Z","signature_b64":"RKU3aUImfxi8U9dh8Nz2ad4HjYDAXeKG8Jn6/bYmFcVLtbeDnGumQS7QR5P/rUyw/EDlb5YN7qtdcdmyIgQRAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3115662699ff230717004e147b4b2a80b9f0b462057cf0c7d1bf94bb13b54ab0","last_reissued_at":"2026-07-05T02:25:10.321719Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:25:10.321719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.09361","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:25:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hqW5a79/Gnd/bj8Q4FqEq/U8TwbJS49YCS9xteUzcLyA5W/ILmPCo0BaiaXyu3iKPEfNP3w4ygbe2EQV68YnDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T14:51:15.109762Z"},"content_sha256":"1f85d9610ae1e2f845a64cfca204abbf36a314ce26c842769416b5b527a8c476","schema_version":"1.0","event_id":"sha256:1f85d9610ae1e2f845a64cfca204abbf36a314ce26c842769416b5b527a8c476"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:GEKWMJUZ74RQOFYAJYKHWSZKQC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gradient Free Minimax Optimization: Variance Reduction and Faster Convergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"H. Vincent Poor, Tengyu Xu, Yingbin Liang, Zhe Wang","submitted_at":"2020-06-16T17:55:46Z","abstract_excerpt":"Many important machine learning applications amount to solving minimax optimization problems, and in many cases there is no access to the gradient information, but only the function values. In this paper, we focus on such a gradient-free setting, and consider the nonconvex-strongly-concave minimax stochastic optimization problem. In the literature, various zeroth-order (i.e., gradient-free) minimax methods have been proposed, but none of them achieve the potentially feasible computational complexity of $\\mathcal{O}(\\epsilon^{-3})$ suggested by the stochastic nonconvex minimization theorem. In "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.09361","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/2006.09361/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":"2026-07-05T02:25:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xw7eVEVoPE2qqe6V3vbpg/y3l5Kb0WmvLhsuqTx/qrYNYMUXG/Re4liXLSLrY08c2aBI4LR68GoTEwmaJmnLAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T14:51:15.110623Z"},"content_sha256":"fc8150cd87a17e328068fac53bd139e78eaf79c47811adc6af6f7aeeaba37428","schema_version":"1.0","event_id":"sha256:fc8150cd87a17e328068fac53bd139e78eaf79c47811adc6af6f7aeeaba37428"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GEKWMJUZ74RQOFYAJYKHWSZKQC/bundle.json","state_url":"https://pith.science/pith/GEKWMJUZ74RQOFYAJYKHWSZKQC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GEKWMJUZ74RQOFYAJYKHWSZKQC/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":"2026-08-14T14:51:15Z","links":{"resolver":"https://pith.science/pith/GEKWMJUZ74RQOFYAJYKHWSZKQC","bundle":"https://pith.science/pith/GEKWMJUZ74RQOFYAJYKHWSZKQC/bundle.json","state":"https://pith.science/pith/GEKWMJUZ74RQOFYAJYKHWSZKQC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GEKWMJUZ74RQOFYAJYKHWSZKQC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:GEKWMJUZ74RQOFYAJYKHWSZKQC","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":"8d45215df13939f44f35db8f3306e450e4b33a5a858a492223573c8e87b5a62c","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-06-16T17:55:46Z","title_canon_sha256":"b9c7e3a68b0cf3d0ad2d34670a2e48a7a2926834484322ddbccb4dc84c13d844"},"schema_version":"1.0","source":{"id":"2006.09361","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.09361","created_at":"2026-07-05T02:25:10Z"},{"alias_kind":"arxiv_version","alias_value":"2006.09361v3","created_at":"2026-07-05T02:25:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.09361","created_at":"2026-07-05T02:25:10Z"},{"alias_kind":"pith_short_12","alias_value":"GEKWMJUZ74RQ","created_at":"2026-07-05T02:25:10Z"},{"alias_kind":"pith_short_16","alias_value":"GEKWMJUZ74RQOFYA","created_at":"2026-07-05T02:25:10Z"},{"alias_kind":"pith_short_8","alias_value":"GEKWMJUZ","created_at":"2026-07-05T02:25:10Z"}],"graph_snapshots":[{"event_id":"sha256:fc8150cd87a17e328068fac53bd139e78eaf79c47811adc6af6f7aeeaba37428","target":"graph","created_at":"2026-07-05T02:25:10Z","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/2006.09361/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Many important machine learning applications amount to solving minimax optimization problems, and in many cases there is no access to the gradient information, but only the function values. In this paper, we focus on such a gradient-free setting, and consider the nonconvex-strongly-concave minimax stochastic optimization problem. In the literature, various zeroth-order (i.e., gradient-free) minimax methods have been proposed, but none of them achieve the potentially feasible computational complexity of $\\mathcal{O}(\\epsilon^{-3})$ suggested by the stochastic nonconvex minimization theorem. In ","authors_text":"H. Vincent Poor, Tengyu Xu, Yingbin Liang, Zhe Wang","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-06-16T17:55:46Z","title":"Gradient Free Minimax Optimization: Variance Reduction and Faster Convergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.09361","kind":"arxiv","version":3},"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":"sha256:1f85d9610ae1e2f845a64cfca204abbf36a314ce26c842769416b5b527a8c476","target":"record","created_at":"2026-07-05T02:25:10Z","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":"8d45215df13939f44f35db8f3306e450e4b33a5a858a492223573c8e87b5a62c","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-06-16T17:55:46Z","title_canon_sha256":"b9c7e3a68b0cf3d0ad2d34670a2e48a7a2926834484322ddbccb4dc84c13d844"},"schema_version":"1.0","source":{"id":"2006.09361","kind":"arxiv","version":3}},"canonical_sha256":"3115662699ff230717004e147b4b2a80b9f0b462057cf0c7d1bf94bb13b54ab0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3115662699ff230717004e147b4b2a80b9f0b462057cf0c7d1bf94bb13b54ab0","first_computed_at":"2026-07-05T02:25:10.321719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:25:10.321719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RKU3aUImfxi8U9dh8Nz2ad4HjYDAXeKG8Jn6/bYmFcVLtbeDnGumQS7QR5P/rUyw/EDlb5YN7qtdcdmyIgQRAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:25:10.322123Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.09361","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f85d9610ae1e2f845a64cfca204abbf36a314ce26c842769416b5b527a8c476","sha256:fc8150cd87a17e328068fac53bd139e78eaf79c47811adc6af6f7aeeaba37428"],"state_sha256":"3a0da07a1eda3698e79ec91fdbdb966bd4fc127282897c16e359afcedffa23d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uTuwft/dcofyd8C1Vd2N3lG4v1xHq1PCnIarYSOxOuQ6KcPunBqQiFFAm+K55WSHZVatHN9fSg+Y0JKpDUrOAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T14:51:15.117728Z","bundle_sha256":"50c6f226fdc2c0c8efb34b2f8682f825bbafa1f03392abbc02097f588d992c19"}}