{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:UB3MTVNL5FBFVRXQ7C4JLFQR5G","short_pith_number":"pith:UB3MTVNL","canonical_record":{"source":{"id":"1309.5549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-22T01:35:43Z","cross_cats_sorted":["cs.CC","stat.ML"],"title_canon_sha256":"ae5760b0826f6005c093859dc6c5159ac786db62a17a87b62d63ced5f5e4fe65","abstract_canon_sha256":"8996f2deade05a31ebbec91934ab08717d96546fa2343f4232744cdbb62d60c2"},"schema_version":"1.0"},"canonical_sha256":"a076c9d5abe9425ac6f0f8b8959611e9a4360f6d4009b9c12ec30866a5fa1ab4","source":{"kind":"arxiv","id":"1309.5549","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5549","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5549v1","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5549","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"pith_short_12","alias_value":"UB3MTVNL5FBF","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UB3MTVNL5FBFVRXQ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UB3MTVNL","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:UB3MTVNL5FBFVRXQ7C4JLFQR5G","target":"record","payload":{"canonical_record":{"source":{"id":"1309.5549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-22T01:35:43Z","cross_cats_sorted":["cs.CC","stat.ML"],"title_canon_sha256":"ae5760b0826f6005c093859dc6c5159ac786db62a17a87b62d63ced5f5e4fe65","abstract_canon_sha256":"8996f2deade05a31ebbec91934ab08717d96546fa2343f4232744cdbb62d60c2"},"schema_version":"1.0"},"canonical_sha256":"a076c9d5abe9425ac6f0f8b8959611e9a4360f6d4009b9c12ec30866a5fa1ab4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:22.000669Z","signature_b64":"ThSGeWtxzC7T3KsbmAT9HJQQBfoqXvLJtE96WqotKWEXRsYGM5V2AHywpixtAi+ju7DYQ//GxfizSFywBhNDDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a076c9d5abe9425ac6f0f8b8959611e9a4360f6d4009b9c12ec30866a5fa1ab4","last_reissued_at":"2026-05-18T01:29:21.999933Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:21.999933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.5549","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:29:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1tLjFZUNJzvCHb1ttrYNBFzbCQnPXqMAeoviqdWRlXVa5GqXA97g39qWNBaWZJfEvFXvD1WGOQN4x1/4+c+IDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:39:42.910410Z"},"content_sha256":"57a5dc6a30f73730b2031d4005d892390ced2091c272ff4772f06648e3630c01","schema_version":"1.0","event_id":"sha256:57a5dc6a30f73730b2031d4005d892390ced2091c272ff4772f06648e3630c01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:UB3MTVNL5FBFVRXQ7C4JLFQR5G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","stat.ML"],"primary_cat":"math.OC","authors_text":"Guanghui Lan, Saeed Ghadimi","submitted_at":"2013-09-22T01:35:43Z","abstract_excerpt":"In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems. We establish the complexity of this method for computing an approximate stationary point of a nonlinear programming problem. We also show that this method possesses a nearly optimal rate of convergence if the problem is convex. We discuss a variant of the algorithm which consists of applying a post-optimization phase to evaluate a short list of solutions gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5549","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T01:29:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WD2L3u3lqJU6NBP0+uJer1GDLABLW/3N64qhTgsuGyA2hiSgOU4GIKEH33LzLKuWulqUNXfzXXKgrym1Yoz+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:39:42.911144Z"},"content_sha256":"4701ad935346e538cb66fc0155cfec9f972b670481c0ae7d39f76da6e845fb17","schema_version":"1.0","event_id":"sha256:4701ad935346e538cb66fc0155cfec9f972b670481c0ae7d39f76da6e845fb17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UB3MTVNL5FBFVRXQ7C4JLFQR5G/bundle.json","state_url":"https://pith.science/pith/UB3MTVNL5FBFVRXQ7C4JLFQR5G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UB3MTVNL5FBFVRXQ7C4JLFQR5G/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":"2026-05-25T23:39:42Z","links":{"resolver":"https://pith.science/pith/UB3MTVNL5FBFVRXQ7C4JLFQR5G","bundle":"https://pith.science/pith/UB3MTVNL5FBFVRXQ7C4JLFQR5G/bundle.json","state":"https://pith.science/pith/UB3MTVNL5FBFVRXQ7C4JLFQR5G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UB3MTVNL5FBFVRXQ7C4JLFQR5G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UB3MTVNL5FBFVRXQ7C4JLFQR5G","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":"8996f2deade05a31ebbec91934ab08717d96546fa2343f4232744cdbb62d60c2","cross_cats_sorted":["cs.CC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-22T01:35:43Z","title_canon_sha256":"ae5760b0826f6005c093859dc6c5159ac786db62a17a87b62d63ced5f5e4fe65"},"schema_version":"1.0","source":{"id":"1309.5549","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5549","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5549v1","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5549","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"pith_short_12","alias_value":"UB3MTVNL5FBF","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UB3MTVNL5FBFVRXQ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UB3MTVNL","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:4701ad935346e538cb66fc0155cfec9f972b670481c0ae7d39f76da6e845fb17","target":"graph","created_at":"2026-05-18T01:29:22Z","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"},"paper":{"abstract_excerpt":"In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems. We establish the complexity of this method for computing an approximate stationary point of a nonlinear programming problem. We also show that this method possesses a nearly optimal rate of convergence if the problem is convex. We discuss a variant of the algorithm which consists of applying a post-optimization phase to evaluate a short list of solutions gene","authors_text":"Guanghui Lan, Saeed Ghadimi","cross_cats":["cs.CC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-22T01:35:43Z","title":"Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5549","kind":"arxiv","version":1},"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":"sha256:57a5dc6a30f73730b2031d4005d892390ced2091c272ff4772f06648e3630c01","target":"record","created_at":"2026-05-18T01:29:22Z","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":"8996f2deade05a31ebbec91934ab08717d96546fa2343f4232744cdbb62d60c2","cross_cats_sorted":["cs.CC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-22T01:35:43Z","title_canon_sha256":"ae5760b0826f6005c093859dc6c5159ac786db62a17a87b62d63ced5f5e4fe65"},"schema_version":"1.0","source":{"id":"1309.5549","kind":"arxiv","version":1}},"canonical_sha256":"a076c9d5abe9425ac6f0f8b8959611e9a4360f6d4009b9c12ec30866a5fa1ab4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a076c9d5abe9425ac6f0f8b8959611e9a4360f6d4009b9c12ec30866a5fa1ab4","first_computed_at":"2026-05-18T01:29:21.999933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:21.999933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ThSGeWtxzC7T3KsbmAT9HJQQBfoqXvLJtE96WqotKWEXRsYGM5V2AHywpixtAi+ju7DYQ//GxfizSFywBhNDDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:22.000669Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5549","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57a5dc6a30f73730b2031d4005d892390ced2091c272ff4772f06648e3630c01","sha256:4701ad935346e538cb66fc0155cfec9f972b670481c0ae7d39f76da6e845fb17"],"state_sha256":"4896c685967463daa5d79706972eead193f02e7b59cbbccf1553787fbfe1a85f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u5b15n6QYcWltySxPeCysmAyZiJJ23Gt0eBfGwr1xTB7LBzJY0HD/MBG47FXjcSVkzYi/3WF3KSShscuMCKwDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:39:42.915010Z","bundle_sha256":"18eb7e5734d362d5410b4c747c7771e3ec1644bdda7f79209b5e6a152dc40766"}}