{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:OBK7PIKWJP4BELSE2BGW7NNAQT","short_pith_number":"pith:OBK7PIKW","canonical_record":{"source":{"id":"1710.09554","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-10-26T06:10:44Z","cross_cats_sorted":["cs.AI","math.OC"],"title_canon_sha256":"5df220614ac885afaf110d2b2f09066a43dc4d4ff6e74288557320920b3cf490","abstract_canon_sha256":"05007812ecc175dbd985e9debd7b4603314bc5da2f9037fe964f5c203f841d93"},"schema_version":"1.0"},"canonical_sha256":"7055f7a1564bf8122e44d04d6fb5a084ec93b261cda9e0712063dd78dc3eae61","source":{"kind":"arxiv","id":"1710.09554","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.09554","created_at":"2026-05-18T00:31:56Z"},{"alias_kind":"arxiv_version","alias_value":"1710.09554v1","created_at":"2026-05-18T00:31:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09554","created_at":"2026-05-18T00:31:56Z"},{"alias_kind":"pith_short_12","alias_value":"OBK7PIKWJP4B","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OBK7PIKWJP4BELSE","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OBK7PIKW","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:OBK7PIKWJP4BELSE2BGW7NNAQT","target":"record","payload":{"canonical_record":{"source":{"id":"1710.09554","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-10-26T06:10:44Z","cross_cats_sorted":["cs.AI","math.OC"],"title_canon_sha256":"5df220614ac885afaf110d2b2f09066a43dc4d4ff6e74288557320920b3cf490","abstract_canon_sha256":"05007812ecc175dbd985e9debd7b4603314bc5da2f9037fe964f5c203f841d93"},"schema_version":"1.0"},"canonical_sha256":"7055f7a1564bf8122e44d04d6fb5a084ec93b261cda9e0712063dd78dc3eae61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:56.908733Z","signature_b64":"qIb78tkErc6QN2QQjJkxNDeWypQElqCPhSyhfAhf+UZ2s04pm8crannc/SAmQG9skPkLiSM/+GxXfD6OAUwJDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7055f7a1564bf8122e44d04d6fb5a084ec93b261cda9e0712063dd78dc3eae61","last_reissued_at":"2026-05-18T00:31:56.908326Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:56.908326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.09554","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":"2026-05-18T00:31:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pEi2oEhWAtVjpn/SB7Q8Fhes8GS9OQC8qhvTufs0i/nNpdO0e6jPt0ClwJGsaMLY1gCOlAFSeBAs+f/YgiOSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:48:00.791114Z"},"content_sha256":"c10fb5aa501b334b3d2642e94b1c1ccc2162842a7d677adb08350bf9cfcfb768","schema_version":"1.0","event_id":"sha256:c10fb5aa501b334b3d2642e94b1c1ccc2162842a7d677adb08350bf9cfcfb768"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:OBK7PIKWJP4BELSE2BGW7NNAQT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Duality-free Methods for Stochastic Composition Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","math.OC"],"primary_cat":"stat.ML","authors_text":"Dacheng Tao, Ji Liu, Liu Liu","submitted_at":"2017-10-26T06:10:44Z","abstract_excerpt":"We consider the composition optimization with two expected-value functions in the form of $\\frac{1}{n}\\sum\\nolimits_{i = 1}^n F_i(\\frac{1}{m}\\sum\\nolimits_{j = 1}^m G_j(x))+R(x)$, { which formulates many important problems in statistical learning and machine learning such as solving Bellman equations in reinforcement learning and nonlinear embedding}. Full Gradient or classical stochastic gradient descent based optimization algorithms are unsuitable or computationally expensive to solve this problem due to the inner expectation $\\frac{1}{m}\\sum\\nolimits_{j = 1}^m G_j(x)$. We propose a duality-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09554","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":"2026-05-18T00:31:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I4QSzSfhe7FZaAjHdBNApuAfn/8UjORzG3HrE4TufsaINxCjEHQMMiDyJjp44ciDEkOdoMtV3S/qU8DvIKJ9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:48:00.791480Z"},"content_sha256":"1e024fa020997baaa645afe54674cecea653b9a0f7d488ed070e65ba43359a93","schema_version":"1.0","event_id":"sha256:1e024fa020997baaa645afe54674cecea653b9a0f7d488ed070e65ba43359a93"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OBK7PIKWJP4BELSE2BGW7NNAQT/bundle.json","state_url":"https://pith.science/pith/OBK7PIKWJP4BELSE2BGW7NNAQT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OBK7PIKWJP4BELSE2BGW7NNAQT/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":"2026-06-01T07:48:00Z","links":{"resolver":"https://pith.science/pith/OBK7PIKWJP4BELSE2BGW7NNAQT","bundle":"https://pith.science/pith/OBK7PIKWJP4BELSE2BGW7NNAQT/bundle.json","state":"https://pith.science/pith/OBK7PIKWJP4BELSE2BGW7NNAQT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OBK7PIKWJP4BELSE2BGW7NNAQT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OBK7PIKWJP4BELSE2BGW7NNAQT","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":"05007812ecc175dbd985e9debd7b4603314bc5da2f9037fe964f5c203f841d93","cross_cats_sorted":["cs.AI","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-10-26T06:10:44Z","title_canon_sha256":"5df220614ac885afaf110d2b2f09066a43dc4d4ff6e74288557320920b3cf490"},"schema_version":"1.0","source":{"id":"1710.09554","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.09554","created_at":"2026-05-18T00:31:56Z"},{"alias_kind":"arxiv_version","alias_value":"1710.09554v1","created_at":"2026-05-18T00:31:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09554","created_at":"2026-05-18T00:31:56Z"},{"alias_kind":"pith_short_12","alias_value":"OBK7PIKWJP4B","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OBK7PIKWJP4BELSE","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OBK7PIKW","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:1e024fa020997baaa645afe54674cecea653b9a0f7d488ed070e65ba43359a93","target":"graph","created_at":"2026-05-18T00:31:56Z","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":"We consider the composition optimization with two expected-value functions in the form of $\\frac{1}{n}\\sum\\nolimits_{i = 1}^n F_i(\\frac{1}{m}\\sum\\nolimits_{j = 1}^m G_j(x))+R(x)$, { which formulates many important problems in statistical learning and machine learning such as solving Bellman equations in reinforcement learning and nonlinear embedding}. Full Gradient or classical stochastic gradient descent based optimization algorithms are unsuitable or computationally expensive to solve this problem due to the inner expectation $\\frac{1}{m}\\sum\\nolimits_{j = 1}^m G_j(x)$. We propose a duality-","authors_text":"Dacheng Tao, Ji Liu, Liu Liu","cross_cats":["cs.AI","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-10-26T06:10:44Z","title":"Duality-free Methods for Stochastic Composition Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09554","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:c10fb5aa501b334b3d2642e94b1c1ccc2162842a7d677adb08350bf9cfcfb768","target":"record","created_at":"2026-05-18T00:31:56Z","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":"05007812ecc175dbd985e9debd7b4603314bc5da2f9037fe964f5c203f841d93","cross_cats_sorted":["cs.AI","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-10-26T06:10:44Z","title_canon_sha256":"5df220614ac885afaf110d2b2f09066a43dc4d4ff6e74288557320920b3cf490"},"schema_version":"1.0","source":{"id":"1710.09554","kind":"arxiv","version":1}},"canonical_sha256":"7055f7a1564bf8122e44d04d6fb5a084ec93b261cda9e0712063dd78dc3eae61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7055f7a1564bf8122e44d04d6fb5a084ec93b261cda9e0712063dd78dc3eae61","first_computed_at":"2026-05-18T00:31:56.908326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:56.908326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qIb78tkErc6QN2QQjJkxNDeWypQElqCPhSyhfAhf+UZ2s04pm8crannc/SAmQG9skPkLiSM/+GxXfD6OAUwJDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:56.908733Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.09554","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c10fb5aa501b334b3d2642e94b1c1ccc2162842a7d677adb08350bf9cfcfb768","sha256:1e024fa020997baaa645afe54674cecea653b9a0f7d488ed070e65ba43359a93"],"state_sha256":"ce63a8862a03ff143725b16c139040be29670f5c2f7f6fb12e25503d5ec41992"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dFU6tmY10TtzXUVKVTj0j27XFHf20dS4WyyStD58nymy8GLuIhxaguMXeRFbSNOWJkExsymjCV6hbjLWUolqAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:48:00.793434Z","bundle_sha256":"147a214c2753a5ba1032d7c70f1d0e6543be5a4b7c65ae61f2017e632ad3685e"}}