{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:P757FIDLHNXMYCV36565WGDCGG","short_pith_number":"pith:P757FIDL","schema_version":"1.0","canonical_sha256":"7ffbf2a06b3b6ecc0abbf77ddb18623185da2a8b37133f5118bff2b10929c368","source":{"kind":"arxiv","id":"2110.12459","version":2},"attestation_state":"computed","paper":{"title":"Non-convex Distributionally Robust Optimization: Non-asymptotic Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Bohang Zhang, Haiyang Wang, Jikai Jin, Liwei Wang","submitted_at":"2021-10-24T14:56:38Z","abstract_excerpt":"Distributionally robust optimization (DRO) is a widely-used approach to learn models that are robust against distribution shift. Compared with the standard optimization setting, the objective function in DRO is more difficult to optimize, and most of the existing theoretical results make strong assumptions on the loss function. In this work we bridge the gap by studying DRO algorithms for general smooth non-convex losses. By carefully exploiting the specific form of the DRO objective, we are able to provide non-asymptotic convergence guarantees even though the objective function is possibly no"},"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":"2110.12459","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-10-24T14:56:38Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"e42c04e30f039654160d92ce2394c3228c583a4c607da949041ba75aaafb4d37","abstract_canon_sha256":"202a8fff9ee21d29dc0c0dcbfb984c6b679cdc29d8f318f9f5eb11aaaa81a4ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:25:35.427222Z","signature_b64":"R6YWG83H2vxd9rrhs4NYK6vMSvXU8QVcF8DVWXYwU634Cv5OkrZuc6y6MLJkh2IYJfwwTghrLLpRvFD90z4IDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ffbf2a06b3b6ecc0abbf77ddb18623185da2a8b37133f5118bff2b10929c368","last_reissued_at":"2026-07-05T03:25:35.426655Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:25:35.426655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-convex Distributionally Robust Optimization: Non-asymptotic Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Bohang Zhang, Haiyang Wang, Jikai Jin, Liwei Wang","submitted_at":"2021-10-24T14:56:38Z","abstract_excerpt":"Distributionally robust optimization (DRO) is a widely-used approach to learn models that are robust against distribution shift. Compared with the standard optimization setting, the objective function in DRO is more difficult to optimize, and most of the existing theoretical results make strong assumptions on the loss function. In this work we bridge the gap by studying DRO algorithms for general smooth non-convex losses. By carefully exploiting the specific form of the DRO objective, we are able to provide non-asymptotic convergence guarantees even though the objective function is possibly no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.12459","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/2110.12459/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":"2110.12459","created_at":"2026-07-05T03:25:35.426731+00:00"},{"alias_kind":"arxiv_version","alias_value":"2110.12459v2","created_at":"2026-07-05T03:25:35.426731+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.12459","created_at":"2026-07-05T03:25:35.426731+00:00"},{"alias_kind":"pith_short_12","alias_value":"P757FIDLHNXM","created_at":"2026-07-05T03:25:35.426731+00:00"},{"alias_kind":"pith_short_16","alias_value":"P757FIDLHNXMYCV3","created_at":"2026-07-05T03:25:35.426731+00:00"},{"alias_kind":"pith_short_8","alias_value":"P757FIDL","created_at":"2026-07-05T03:25:35.426731+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/P757FIDLHNXMYCV36565WGDCGG","json":"https://pith.science/pith/P757FIDLHNXMYCV36565WGDCGG.json","graph_json":"https://pith.science/api/pith-number/P757FIDLHNXMYCV36565WGDCGG/graph.json","events_json":"https://pith.science/api/pith-number/P757FIDLHNXMYCV36565WGDCGG/events.json","paper":"https://pith.science/paper/P757FIDL"},"agent_actions":{"view_html":"https://pith.science/pith/P757FIDLHNXMYCV36565WGDCGG","download_json":"https://pith.science/pith/P757FIDLHNXMYCV36565WGDCGG.json","view_paper":"https://pith.science/paper/P757FIDL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2110.12459&json=true","fetch_graph":"https://pith.science/api/pith-number/P757FIDLHNXMYCV36565WGDCGG/graph.json","fetch_events":"https://pith.science/api/pith-number/P757FIDLHNXMYCV36565WGDCGG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P757FIDLHNXMYCV36565WGDCGG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P757FIDLHNXMYCV36565WGDCGG/action/storage_attestation","attest_author":"https://pith.science/pith/P757FIDLHNXMYCV36565WGDCGG/action/author_attestation","sign_citation":"https://pith.science/pith/P757FIDLHNXMYCV36565WGDCGG/action/citation_signature","submit_replication":"https://pith.science/pith/P757FIDLHNXMYCV36565WGDCGG/action/replication_record"}},"created_at":"2026-07-05T03:25:35.426731+00:00","updated_at":"2026-07-05T03:25:35.426731+00:00"}