{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:JQN7BY4PLWUB5UWPYWWQK567IC","short_pith_number":"pith:JQN7BY4P","canonical_record":{"source":{"id":"2403.03562","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-03-06T09:14:24Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"2f5941aa8248976481545c1cb669628f73f4675c42df3dc10dd18b159fb407ad","abstract_canon_sha256":"f05e9422488963628b27f7218bfd430fcc94bb1e863fdd5e3a98fc696c4ff16f"},"schema_version":"1.0"},"canonical_sha256":"4c1bf0e38f5da81ed2cfc5ad0577df40a3103bddf7396c35916e8ebea339d2d7","source":{"kind":"arxiv","id":"2403.03562","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.03562","created_at":"2026-07-05T09:09:19Z"},{"alias_kind":"arxiv_version","alias_value":"2403.03562v2","created_at":"2026-07-05T09:09:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.03562","created_at":"2026-07-05T09:09:19Z"},{"alias_kind":"pith_short_12","alias_value":"JQN7BY4PLWUB","created_at":"2026-07-05T09:09:19Z"},{"alias_kind":"pith_short_16","alias_value":"JQN7BY4PLWUB5UWP","created_at":"2026-07-05T09:09:19Z"},{"alias_kind":"pith_short_8","alias_value":"JQN7BY4P","created_at":"2026-07-05T09:09:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:JQN7BY4PLWUB5UWPYWWQK567IC","target":"record","payload":{"canonical_record":{"source":{"id":"2403.03562","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-03-06T09:14:24Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"2f5941aa8248976481545c1cb669628f73f4675c42df3dc10dd18b159fb407ad","abstract_canon_sha256":"f05e9422488963628b27f7218bfd430fcc94bb1e863fdd5e3a98fc696c4ff16f"},"schema_version":"1.0"},"canonical_sha256":"4c1bf0e38f5da81ed2cfc5ad0577df40a3103bddf7396c35916e8ebea339d2d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:09:19.894297Z","signature_b64":"NO3dojq5FyE33/K/3vdLpJTEgSDC1DwXih5gQBwbXkqxq6RZZHGNeFIw6uIwc4nq0PN7wpkKJ/YZuqW1AOqkBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c1bf0e38f5da81ed2cfc5ad0577df40a3103bddf7396c35916e8ebea339d2d7","last_reissued_at":"2026-07-05T09:09:19.893808Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:09:19.893808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.03562","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":"2026-07-05T09:09:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8YQqGHWx9czpKi98hx7OtKuCdwEZ4VkCIRep3+ecvb8lw2Z9Q6OtNAZp7y7YZjen7fWZwNhY4GTUfSR/Iy7NBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T01:08:51.288880Z"},"content_sha256":"c936c183a4f7db02e32b12246d40efec79fb8333f550d4d143e90b63c99c757d","schema_version":"1.0","event_id":"sha256:c936c183a4f7db02e32b12246d40efec79fb8333f550d4d143e90b63c99c757d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:JQN7BY4PLWUB5UWPYWWQK567IC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient Algorithms for Empirical Group Distributionally Robust Optimization and Beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Dingzhi Yu, Lijun Zhang, Wei Jiang, Yunuo Cai","submitted_at":"2024-03-06T09:14:24Z","abstract_excerpt":"In this paper, we investigate the empirical counterpart of Group Distributionally Robust Optimization (GDRO), which aims to minimize the maximal empirical risk across $m$ distinct groups. We formulate empirical GDRO as a $\\textit{two-level}$ finite-sum convex-concave minimax optimization problem and develop an algorithm called ALEG to benefit from its special structure. ALEG is a double-looped stochastic primal-dual algorithm that incorporates variance reduction techniques into a modified mirror prox routine. To exploit the two-level finite-sum structure, we propose a simple group sampling str"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.03562","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/2403.03562/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":"2026-07-05T09:09:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z9clc0z34T2BurJGYs88v105KIR9w4e14bxWk9sJTIg8xuy7nPgkp5kR5hE/NoluytupMf2vUQ2SMJ40Os9xBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T01:08:51.289366Z"},"content_sha256":"ebb0535bb2f41fffbf765fa2c63b66d2b74463bb3a1e805a29f5e4096659ed8c","schema_version":"1.0","event_id":"sha256:ebb0535bb2f41fffbf765fa2c63b66d2b74463bb3a1e805a29f5e4096659ed8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JQN7BY4PLWUB5UWPYWWQK567IC/bundle.json","state_url":"https://pith.science/pith/JQN7BY4PLWUB5UWPYWWQK567IC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JQN7BY4PLWUB5UWPYWWQK567IC/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":"2026-08-06T01:08:51Z","links":{"resolver":"https://pith.science/pith/JQN7BY4PLWUB5UWPYWWQK567IC","bundle":"https://pith.science/pith/JQN7BY4PLWUB5UWPYWWQK567IC/bundle.json","state":"https://pith.science/pith/JQN7BY4PLWUB5UWPYWWQK567IC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JQN7BY4PLWUB5UWPYWWQK567IC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:JQN7BY4PLWUB5UWPYWWQK567IC","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":"f05e9422488963628b27f7218bfd430fcc94bb1e863fdd5e3a98fc696c4ff16f","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-03-06T09:14:24Z","title_canon_sha256":"2f5941aa8248976481545c1cb669628f73f4675c42df3dc10dd18b159fb407ad"},"schema_version":"1.0","source":{"id":"2403.03562","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.03562","created_at":"2026-07-05T09:09:19Z"},{"alias_kind":"arxiv_version","alias_value":"2403.03562v2","created_at":"2026-07-05T09:09:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.03562","created_at":"2026-07-05T09:09:19Z"},{"alias_kind":"pith_short_12","alias_value":"JQN7BY4PLWUB","created_at":"2026-07-05T09:09:19Z"},{"alias_kind":"pith_short_16","alias_value":"JQN7BY4PLWUB5UWP","created_at":"2026-07-05T09:09:19Z"},{"alias_kind":"pith_short_8","alias_value":"JQN7BY4P","created_at":"2026-07-05T09:09:19Z"}],"graph_snapshots":[{"event_id":"sha256:ebb0535bb2f41fffbf765fa2c63b66d2b74463bb3a1e805a29f5e4096659ed8c","target":"graph","created_at":"2026-07-05T09:09:19Z","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/2403.03562/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate the empirical counterpart of Group Distributionally Robust Optimization (GDRO), which aims to minimize the maximal empirical risk across $m$ distinct groups. We formulate empirical GDRO as a $\\textit{two-level}$ finite-sum convex-concave minimax optimization problem and develop an algorithm called ALEG to benefit from its special structure. ALEG is a double-looped stochastic primal-dual algorithm that incorporates variance reduction techniques into a modified mirror prox routine. To exploit the two-level finite-sum structure, we propose a simple group sampling str","authors_text":"Dingzhi Yu, Lijun Zhang, Wei Jiang, Yunuo Cai","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-03-06T09:14:24Z","title":"Efficient Algorithms for Empirical Group Distributionally Robust Optimization and Beyond"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.03562","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:c936c183a4f7db02e32b12246d40efec79fb8333f550d4d143e90b63c99c757d","target":"record","created_at":"2026-07-05T09:09:19Z","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":"f05e9422488963628b27f7218bfd430fcc94bb1e863fdd5e3a98fc696c4ff16f","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-03-06T09:14:24Z","title_canon_sha256":"2f5941aa8248976481545c1cb669628f73f4675c42df3dc10dd18b159fb407ad"},"schema_version":"1.0","source":{"id":"2403.03562","kind":"arxiv","version":2}},"canonical_sha256":"4c1bf0e38f5da81ed2cfc5ad0577df40a3103bddf7396c35916e8ebea339d2d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c1bf0e38f5da81ed2cfc5ad0577df40a3103bddf7396c35916e8ebea339d2d7","first_computed_at":"2026-07-05T09:09:19.893808Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:09:19.893808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NO3dojq5FyE33/K/3vdLpJTEgSDC1DwXih5gQBwbXkqxq6RZZHGNeFIw6uIwc4nq0PN7wpkKJ/YZuqW1AOqkBw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:09:19.894297Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.03562","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c936c183a4f7db02e32b12246d40efec79fb8333f550d4d143e90b63c99c757d","sha256:ebb0535bb2f41fffbf765fa2c63b66d2b74463bb3a1e805a29f5e4096659ed8c"],"state_sha256":"e51a7427d384b76132f456f9bda9e2ffc9fe3bc2329db359ecdc305b24370330"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1y3y1Mj+GYcMR7Tj3SV3e79nNJlnSA6N62AR4fFtEK/zL8XpNngaQuoxLpzfsz7+uzKK8bFYPpeRhWW+QnryCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T01:08:51.292751Z","bundle_sha256":"c1ba1f0078dc4e4819b7ff008a56930782221d406d82cba21d589c29debee060"}}