{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OTSGXAZE2S6ZEV3F7656BUV52O","short_pith_number":"pith:OTSGXAZE","canonical_record":{"source":{"id":"1801.03600","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-11T00:45:49Z","cross_cats_sorted":[],"title_canon_sha256":"fc949573981d6028b09ec27ab9571f3e211b32ab9cc5ed03d04665f32c657016","abstract_canon_sha256":"581ebd7f0b597904844f160d929c35f0ef45067fa433f0eeb8ffc4412104ecfe"},"schema_version":"1.0"},"canonical_sha256":"74e46b8324d4bd925765ffbbe0d2bdd3848e4224cd6ae4371dfeda0d4079fc8a","source":{"kind":"arxiv","id":"1801.03600","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.03600","created_at":"2026-05-18T00:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"1801.03600v2","created_at":"2026-05-18T00:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.03600","created_at":"2026-05-18T00:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"OTSGXAZE2S6Z","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OTSGXAZE2S6ZEV3F","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OTSGXAZE","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OTSGXAZE2S6ZEV3F7656BUV52O","target":"record","payload":{"canonical_record":{"source":{"id":"1801.03600","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-11T00:45:49Z","cross_cats_sorted":[],"title_canon_sha256":"fc949573981d6028b09ec27ab9571f3e211b32ab9cc5ed03d04665f32c657016","abstract_canon_sha256":"581ebd7f0b597904844f160d929c35f0ef45067fa433f0eeb8ffc4412104ecfe"},"schema_version":"1.0"},"canonical_sha256":"74e46b8324d4bd925765ffbbe0d2bdd3848e4224cd6ae4371dfeda0d4079fc8a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:12.355550Z","signature_b64":"6VMlZnSrDZq5ajxaj+L1VWVg3srPPYJANiy0nNUTbKH0cgGYWDS9WwtdGv1dtsEa4VhIw5uMb1aBT8lWemQ7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74e46b8324d4bd925765ffbbe0d2bdd3848e4224cd6ae4371dfeda0d4079fc8a","last_reissued_at":"2026-05-18T00:26:12.355099Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:12.355099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.03600","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":"2026-05-18T00:26:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HH1EbumPKieQiLEgL/8WhN4gJ56fN1vSCyM4GiD84UKomq9swO06UjvNDXxQ8klA7DJYLYIgC8Wyhz8KQhQRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T05:49:57.099754Z"},"content_sha256":"12da3039c116013809cd34138831320a88c47e827507dbdebbb9954c49987c70","schema_version":"1.0","event_id":"sha256:12da3039c116013809cd34138831320a88c47e827507dbdebbb9954c49987c70"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OTSGXAZE2S6ZEV3F7656BUV52O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-Level Stochastic Gradient Methods for Nested Composition Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Ethan X. Fang, Mengdi Wang, Shuoguang Yang","submitted_at":"2018-01-11T00:45:49Z","abstract_excerpt":"Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level expectations. In this paper, we consider the multi-level compositional optimization problem that involves compositions of multi-level component functions and nested expectations over a random path. It finds applications in risk-averse optimization and sequential planning. We propose a class of multi-level stochastic gradient methods that are motivated from t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03600","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":""},"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":"2026-05-18T00:26:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oqAmVaTR4M0WMaXWmSQGhWGhc+cQBRisWaLZ9aLfKA0h/173cW4+S0miSFnGbs99suJgZlRNBOHZjxKvpu0lBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T05:49:57.100294Z"},"content_sha256":"ad293160494b0ca3507dc9bfd7b7317850b15ce78721daef5d4af4b451367b5e","schema_version":"1.0","event_id":"sha256:ad293160494b0ca3507dc9bfd7b7317850b15ce78721daef5d4af4b451367b5e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OTSGXAZE2S6ZEV3F7656BUV52O/bundle.json","state_url":"https://pith.science/pith/OTSGXAZE2S6ZEV3F7656BUV52O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OTSGXAZE2S6ZEV3F7656BUV52O/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":"2026-06-07T05:49:57Z","links":{"resolver":"https://pith.science/pith/OTSGXAZE2S6ZEV3F7656BUV52O","bundle":"https://pith.science/pith/OTSGXAZE2S6ZEV3F7656BUV52O/bundle.json","state":"https://pith.science/pith/OTSGXAZE2S6ZEV3F7656BUV52O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OTSGXAZE2S6ZEV3F7656BUV52O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OTSGXAZE2S6ZEV3F7656BUV52O","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":"581ebd7f0b597904844f160d929c35f0ef45067fa433f0eeb8ffc4412104ecfe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-11T00:45:49Z","title_canon_sha256":"fc949573981d6028b09ec27ab9571f3e211b32ab9cc5ed03d04665f32c657016"},"schema_version":"1.0","source":{"id":"1801.03600","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.03600","created_at":"2026-05-18T00:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"1801.03600v2","created_at":"2026-05-18T00:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.03600","created_at":"2026-05-18T00:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"OTSGXAZE2S6Z","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OTSGXAZE2S6ZEV3F","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OTSGXAZE","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:ad293160494b0ca3507dc9bfd7b7317850b15ce78721daef5d4af4b451367b5e","target":"graph","created_at":"2026-05-18T00:26:12Z","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":"Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level expectations. In this paper, we consider the multi-level compositional optimization problem that involves compositions of multi-level component functions and nested expectations over a random path. It finds applications in risk-averse optimization and sequential planning. We propose a class of multi-level stochastic gradient methods that are motivated from t","authors_text":"Ethan X. Fang, Mengdi Wang, Shuoguang Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-11T00:45:49Z","title":"Multi-Level Stochastic Gradient Methods for Nested Composition Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03600","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":"sha256:12da3039c116013809cd34138831320a88c47e827507dbdebbb9954c49987c70","target":"record","created_at":"2026-05-18T00:26:12Z","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":"581ebd7f0b597904844f160d929c35f0ef45067fa433f0eeb8ffc4412104ecfe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-11T00:45:49Z","title_canon_sha256":"fc949573981d6028b09ec27ab9571f3e211b32ab9cc5ed03d04665f32c657016"},"schema_version":"1.0","source":{"id":"1801.03600","kind":"arxiv","version":2}},"canonical_sha256":"74e46b8324d4bd925765ffbbe0d2bdd3848e4224cd6ae4371dfeda0d4079fc8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74e46b8324d4bd925765ffbbe0d2bdd3848e4224cd6ae4371dfeda0d4079fc8a","first_computed_at":"2026-05-18T00:26:12.355099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:12.355099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6VMlZnSrDZq5ajxaj+L1VWVg3srPPYJANiy0nNUTbKH0cgGYWDS9WwtdGv1dtsEa4VhIw5uMb1aBT8lWemQ7AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:12.355550Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.03600","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12da3039c116013809cd34138831320a88c47e827507dbdebbb9954c49987c70","sha256:ad293160494b0ca3507dc9bfd7b7317850b15ce78721daef5d4af4b451367b5e"],"state_sha256":"3c3460035439f7852d606c3ba6021bc7b055e6d0592f6f1bd529626932dfcb4d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d3PH4dkDXRc5lg0EKxoQ3YvSWV1FCaiG6Z6qlsZtTx+hQaYezMsSRmDrULLWoJRMyCuzrJrix5hBK43h1ZDcCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T05:49:57.102935Z","bundle_sha256":"63331d968119f82bfd2f3174857c623458a522d0c2ac514d2b081b09560cbdf6"}}