{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:NPOKI4DZ6B3HXFD74MXTXRMMTQ","short_pith_number":"pith:NPOKI4DZ","canonical_record":{"source":{"id":"2201.08518","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2022-01-21T02:46:57Z","cross_cats_sorted":["cs.LG","math.OC","stat.ML","stat.TH"],"title_canon_sha256":"21041fe1be529a5a097a7826f3ac081b7f143f5f12df544c45f81527203b2aa7","abstract_canon_sha256":"09111c6999232db73187dd6e8c483dca401e1c63fd26d0362686df6fe1bd87e8"},"schema_version":"1.0"},"canonical_sha256":"6bdca47079f0767b947fe32f3bc58c9c0c584390050e0f3e1f173244b6c9c442","source":{"kind":"arxiv","id":"2201.08518","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.08518","created_at":"2026-07-05T05:20:09Z"},{"alias_kind":"arxiv_version","alias_value":"2201.08518v2","created_at":"2026-07-05T05:20:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.08518","created_at":"2026-07-05T05:20:09Z"},{"alias_kind":"pith_short_12","alias_value":"NPOKI4DZ6B3H","created_at":"2026-07-05T05:20:09Z"},{"alias_kind":"pith_short_16","alias_value":"NPOKI4DZ6B3HXFD7","created_at":"2026-07-05T05:20:09Z"},{"alias_kind":"pith_short_8","alias_value":"NPOKI4DZ","created_at":"2026-07-05T05:20:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:NPOKI4DZ6B3HXFD74MXTXRMMTQ","target":"record","payload":{"canonical_record":{"source":{"id":"2201.08518","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2022-01-21T02:46:57Z","cross_cats_sorted":["cs.LG","math.OC","stat.ML","stat.TH"],"title_canon_sha256":"21041fe1be529a5a097a7826f3ac081b7f143f5f12df544c45f81527203b2aa7","abstract_canon_sha256":"09111c6999232db73187dd6e8c483dca401e1c63fd26d0362686df6fe1bd87e8"},"schema_version":"1.0"},"canonical_sha256":"6bdca47079f0767b947fe32f3bc58c9c0c584390050e0f3e1f173244b6c9c442","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:20:09.699152Z","signature_b64":"Mj5AKYfMFJ7BHvsVr6IuP+lnRbRzAOUB3GOeLV9x6mKieaOLVb/ZWaz2vbROYGFeubRgUHlR/53K61ObtGNQAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bdca47079f0767b947fe32f3bc58c9c0c584390050e0f3e1f173244b6c9c442","last_reissued_at":"2026-07-05T05:20:09.698602Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:20:09.698602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2201.08518","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":"2026-07-05T05:20:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MQe+lHoAUqH1xa81Dql/SncLjU6rZ6WJth3CxGMEBF8k3+oWrEaZXxFRRDyPi+EJDveHlKW25t6+Fd2ESZajAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T05:00:22.264390Z"},"content_sha256":"b76783a48c148b2171574b218ecd04eee2aa047bef949d9db26152643b3835a9","schema_version":"1.0","event_id":"sha256:b76783a48c148b2171574b218ecd04eee2aa047bef949d9db26152643b3835a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:NPOKI4DZ6B3HXFD74MXTXRMMTQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal variance-reduced stochastic approximation in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.OC","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Koulik Khamaru, Martin J. Wainwright, Michael I. Jordan, Peter L. Bartlett, Wenlong Mou","submitted_at":"2022-01-21T02:46:57Z","abstract_excerpt":"We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. Focusing on a stochastic query model that provides noisy evaluations of the operator, we analyze a variance-reduced stochastic approximation scheme, and establish non-asymptotic bounds for both the operator defect and the estimation error, measured in an arbitrary semi-norm. In contrast to worst-case guarantees, our bounds are instance-dependent, and achieve the local asymptotic minimax risk non-asymptotically. For linear operators, contractivity can be relaxed to multi-step contra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.08518","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/2201.08518/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":"2026-07-05T05:20:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W9XKiN/4SBT8eFuTXY/Kgyyxzo6rBkKkVYxThL8xX2aaSiHvJGuxCYQ/vSGGateGDiQDlwAjWz8VOTupjmHfAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T05:00:22.264781Z"},"content_sha256":"debe15b35df504c49dcc8bf152e8f4906bf15f138b3361d49bf1f64d95b761b7","schema_version":"1.0","event_id":"sha256:debe15b35df504c49dcc8bf152e8f4906bf15f138b3361d49bf1f64d95b761b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NPOKI4DZ6B3HXFD74MXTXRMMTQ/bundle.json","state_url":"https://pith.science/pith/NPOKI4DZ6B3HXFD74MXTXRMMTQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NPOKI4DZ6B3HXFD74MXTXRMMTQ/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":"2026-07-09T05:00:22Z","links":{"resolver":"https://pith.science/pith/NPOKI4DZ6B3HXFD74MXTXRMMTQ","bundle":"https://pith.science/pith/NPOKI4DZ6B3HXFD74MXTXRMMTQ/bundle.json","state":"https://pith.science/pith/NPOKI4DZ6B3HXFD74MXTXRMMTQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NPOKI4DZ6B3HXFD74MXTXRMMTQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:NPOKI4DZ6B3HXFD74MXTXRMMTQ","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":"09111c6999232db73187dd6e8c483dca401e1c63fd26d0362686df6fe1bd87e8","cross_cats_sorted":["cs.LG","math.OC","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2022-01-21T02:46:57Z","title_canon_sha256":"21041fe1be529a5a097a7826f3ac081b7f143f5f12df544c45f81527203b2aa7"},"schema_version":"1.0","source":{"id":"2201.08518","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.08518","created_at":"2026-07-05T05:20:09Z"},{"alias_kind":"arxiv_version","alias_value":"2201.08518v2","created_at":"2026-07-05T05:20:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.08518","created_at":"2026-07-05T05:20:09Z"},{"alias_kind":"pith_short_12","alias_value":"NPOKI4DZ6B3H","created_at":"2026-07-05T05:20:09Z"},{"alias_kind":"pith_short_16","alias_value":"NPOKI4DZ6B3HXFD7","created_at":"2026-07-05T05:20:09Z"},{"alias_kind":"pith_short_8","alias_value":"NPOKI4DZ","created_at":"2026-07-05T05:20:09Z"}],"graph_snapshots":[{"event_id":"sha256:debe15b35df504c49dcc8bf152e8f4906bf15f138b3361d49bf1f64d95b761b7","target":"graph","created_at":"2026-07-05T05:20:09Z","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/2201.08518/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. Focusing on a stochastic query model that provides noisy evaluations of the operator, we analyze a variance-reduced stochastic approximation scheme, and establish non-asymptotic bounds for both the operator defect and the estimation error, measured in an arbitrary semi-norm. In contrast to worst-case guarantees, our bounds are instance-dependent, and achieve the local asymptotic minimax risk non-asymptotically. For linear operators, contractivity can be relaxed to multi-step contra","authors_text":"Koulik Khamaru, Martin J. Wainwright, Michael I. Jordan, Peter L. Bartlett, Wenlong Mou","cross_cats":["cs.LG","math.OC","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2022-01-21T02:46:57Z","title":"Optimal variance-reduced stochastic approximation in Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.08518","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:b76783a48c148b2171574b218ecd04eee2aa047bef949d9db26152643b3835a9","target":"record","created_at":"2026-07-05T05:20:09Z","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":"09111c6999232db73187dd6e8c483dca401e1c63fd26d0362686df6fe1bd87e8","cross_cats_sorted":["cs.LG","math.OC","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2022-01-21T02:46:57Z","title_canon_sha256":"21041fe1be529a5a097a7826f3ac081b7f143f5f12df544c45f81527203b2aa7"},"schema_version":"1.0","source":{"id":"2201.08518","kind":"arxiv","version":2}},"canonical_sha256":"6bdca47079f0767b947fe32f3bc58c9c0c584390050e0f3e1f173244b6c9c442","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bdca47079f0767b947fe32f3bc58c9c0c584390050e0f3e1f173244b6c9c442","first_computed_at":"2026-07-05T05:20:09.698602Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:20:09.698602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mj5AKYfMFJ7BHvsVr6IuP+lnRbRzAOUB3GOeLV9x6mKieaOLVb/ZWaz2vbROYGFeubRgUHlR/53K61ObtGNQAg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:20:09.699152Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.08518","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b76783a48c148b2171574b218ecd04eee2aa047bef949d9db26152643b3835a9","sha256:debe15b35df504c49dcc8bf152e8f4906bf15f138b3361d49bf1f64d95b761b7"],"state_sha256":"ca0d8be741f105792072fe42e6116411d6a7607df8326f5bf592d039500406e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Pa2VQdHHDs9zE8lDLF1Da7IDr6XJ2zMEZCpSfm74Wj0Rh5EwYSf7MQpYAQ7Pj+mHHamNvAl6Vo+TyxYDLi9CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T05:00:22.267375Z","bundle_sha256":"db693a873b499d106b0bb8547ba63b41a2a975a2823e6289e23561e53d692f66"}}