{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:CZ4F3Q7QYYFMH4J4FHDE2YXVPB","short_pith_number":"pith:CZ4F3Q7Q","schema_version":"1.0","canonical_sha256":"16785dc3f0c60ac3f13c29c64d62f57855e5e148b59c32f91bb1fdea09ee59f8","source":{"kind":"arxiv","id":"1812.01094","version":2},"attestation_state":"computed","paper":{"title":"A Single Time-Scale Stochastic Approximation Method for Nested Stochastic Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andrzej Ruszczy\\'nski, Mengdi Wang, Saeed Ghadimi","submitted_at":"2018-12-03T21:58:21Z","abstract_excerpt":"We study constrained nested stochastic optimization problems in which the objective function is a composition of two smooth functions whose exact values and derivatives are not available. We propose a single time-scale stochastic approximation algorithm, which we call the Nested Averaged Stochastic Approximation (NASA), to find an approximate stationary point of the problem. The algorithm has two auxiliary averaged sequences (filters) which estimate the gradient of the composite objective function and the inner function value. By using a special Lyapunov function, we show that NASA achieves th"},"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":"1812.01094","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-03T21:58:21Z","cross_cats_sorted":[],"title_canon_sha256":"3c5c38971e2d34a9243ba757a01785512134dbdb8806067fc417ffa8ea3f91f5","abstract_canon_sha256":"4a0564eae73c3352b818d9b321e97a8c1d95abe4d71acec7081ba55d50526558"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:02:37.512585Z","signature_b64":"VVlKg49F+3tBk/seNFuRF7xMVVnEOinu45SHhECoP+ZxPe3gEmz7MkRlIvRUGGCEvNH5W82S51LPYDb3jQk7Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16785dc3f0c60ac3f13c29c64d62f57855e5e148b59c32f91bb1fdea09ee59f8","last_reissued_at":"2026-07-05T00:02:37.512107Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:02:37.512107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Single Time-Scale Stochastic Approximation Method for Nested Stochastic Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andrzej Ruszczy\\'nski, Mengdi Wang, Saeed Ghadimi","submitted_at":"2018-12-03T21:58:21Z","abstract_excerpt":"We study constrained nested stochastic optimization problems in which the objective function is a composition of two smooth functions whose exact values and derivatives are not available. We propose a single time-scale stochastic approximation algorithm, which we call the Nested Averaged Stochastic Approximation (NASA), to find an approximate stationary point of the problem. The algorithm has two auxiliary averaged sequences (filters) which estimate the gradient of the composite objective function and the inner function value. By using a special Lyapunov function, we show that NASA achieves th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01094","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/1812.01094/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":"1812.01094","created_at":"2026-07-05T00:02:37.512163+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.01094v2","created_at":"2026-07-05T00:02:37.512163+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.01094","created_at":"2026-07-05T00:02:37.512163+00:00"},{"alias_kind":"pith_short_12","alias_value":"CZ4F3Q7QYYFM","created_at":"2026-07-05T00:02:37.512163+00:00"},{"alias_kind":"pith_short_16","alias_value":"CZ4F3Q7QYYFMH4J4","created_at":"2026-07-05T00:02:37.512163+00:00"},{"alias_kind":"pith_short_8","alias_value":"CZ4F3Q7Q","created_at":"2026-07-05T00:02:37.512163+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.11468","citing_title":"Multi-Level Composite Stochastic Optimization via Nested Variance Reduction","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CZ4F3Q7QYYFMH4J4FHDE2YXVPB","json":"https://pith.science/pith/CZ4F3Q7QYYFMH4J4FHDE2YXVPB.json","graph_json":"https://pith.science/api/pith-number/CZ4F3Q7QYYFMH4J4FHDE2YXVPB/graph.json","events_json":"https://pith.science/api/pith-number/CZ4F3Q7QYYFMH4J4FHDE2YXVPB/events.json","paper":"https://pith.science/paper/CZ4F3Q7Q"},"agent_actions":{"view_html":"https://pith.science/pith/CZ4F3Q7QYYFMH4J4FHDE2YXVPB","download_json":"https://pith.science/pith/CZ4F3Q7QYYFMH4J4FHDE2YXVPB.json","view_paper":"https://pith.science/paper/CZ4F3Q7Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.01094&json=true","fetch_graph":"https://pith.science/api/pith-number/CZ4F3Q7QYYFMH4J4FHDE2YXVPB/graph.json","fetch_events":"https://pith.science/api/pith-number/CZ4F3Q7QYYFMH4J4FHDE2YXVPB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CZ4F3Q7QYYFMH4J4FHDE2YXVPB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CZ4F3Q7QYYFMH4J4FHDE2YXVPB/action/storage_attestation","attest_author":"https://pith.science/pith/CZ4F3Q7QYYFMH4J4FHDE2YXVPB/action/author_attestation","sign_citation":"https://pith.science/pith/CZ4F3Q7QYYFMH4J4FHDE2YXVPB/action/citation_signature","submit_replication":"https://pith.science/pith/CZ4F3Q7QYYFMH4J4FHDE2YXVPB/action/replication_record"}},"created_at":"2026-07-05T00:02:37.512163+00:00","updated_at":"2026-07-05T00:02:37.512163+00:00"}