{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:74GYG5BXSCHC4MICCSJCV52FYY","short_pith_number":"pith:74GYG5BX","canonical_record":{"source":{"id":"2412.18518","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2024-12-24T15:55:30Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"f850c9ac83605e79c797f7b0ef97ccb0910ae8c68cb4c711c7e22ad0a9497bfb","abstract_canon_sha256":"95ea6517d5e09edbf3338a1018a91e1200f59d72bcb582abda8923df3b24771f"},"schema_version":"1.0"},"canonical_sha256":"ff0d837437908e2e310214922af745c63fe371f709a704ea3ec024960cc97372","source":{"kind":"arxiv","id":"2412.18518","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.18518","created_at":"2026-07-05T09:53:56Z"},{"alias_kind":"arxiv_version","alias_value":"2412.18518v1","created_at":"2026-07-05T09:53:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.18518","created_at":"2026-07-05T09:53:56Z"},{"alias_kind":"pith_short_12","alias_value":"74GYG5BXSCHC","created_at":"2026-07-05T09:53:56Z"},{"alias_kind":"pith_short_16","alias_value":"74GYG5BXSCHC4MIC","created_at":"2026-07-05T09:53:56Z"},{"alias_kind":"pith_short_8","alias_value":"74GYG5BX","created_at":"2026-07-05T09:53:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:74GYG5BXSCHC4MICCSJCV52FYY","target":"record","payload":{"canonical_record":{"source":{"id":"2412.18518","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2024-12-24T15:55:30Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"f850c9ac83605e79c797f7b0ef97ccb0910ae8c68cb4c711c7e22ad0a9497bfb","abstract_canon_sha256":"95ea6517d5e09edbf3338a1018a91e1200f59d72bcb582abda8923df3b24771f"},"schema_version":"1.0"},"canonical_sha256":"ff0d837437908e2e310214922af745c63fe371f709a704ea3ec024960cc97372","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:53:56.932555Z","signature_b64":"MhnIQ2LfXX3gUHDptB/VNoiU2lausvdIFc21dGwkRFNIbk7KEscTPGEEqkOzgGOkDNGkmVb8uL11DxXBW/5pBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff0d837437908e2e310214922af745c63fe371f709a704ea3ec024960cc97372","last_reissued_at":"2026-07-05T09:53:56.932169Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:53:56.932169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.18518","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":"2026-07-05T09:53:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AFKRxw2fDBU0vijgByQKI7re7MJAi9p25VjqQ2efsj21t7ehK8B8NseogKYl3WRgi98cz/7ZW3eWx0NjPfz5Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T10:36:54.831322Z"},"content_sha256":"ab2e6384e2be00a04c60469fa7b39dc9da1018ed5def3a6071c3b8440eb28097","schema_version":"1.0","event_id":"sha256:ab2e6384e2be00a04c60469fa7b39dc9da1018ed5def3a6071c3b8440eb28097"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:74GYG5BXSCHC4MICCSJCV52FYY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bayesian Optimization of Bilevel Problems","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Juergen Branke, Nursen Aydin, Omer Ekmekcioglu","submitted_at":"2024-12-24T15:55:30Z","abstract_excerpt":"Bilevel optimization, a hierarchical mathematical framework where one optimization problem is nested within another, has emerged as a powerful tool for modeling complex decision-making processes in various fields such as economics, engineering, and machine learning. This paper focuses on bilevel optimization where both upper-level and lower-level functions are black boxes and expensive to evaluate. We propose a Bayesian Optimization framework that models the upper and lower-level functions as Gaussian processes over the combined space of upper and lower-level decisions, allowing us to exploit "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.18518","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.18518/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":"2026-07-05T09:53:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JaA4K6Zs0xfo7r6FmeBnfXg76hcGzon1sFL+pmkPQ9sYz+52LiLKdaHMMQzNJpNy/V9Cjz5bFjoq+u+k/OndDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T10:36:54.831822Z"},"content_sha256":"e693f3cae93b7b4068dcca4337d7d62e3207fd89f2e2e1c5f1f21de8f9924707","schema_version":"1.0","event_id":"sha256:e693f3cae93b7b4068dcca4337d7d62e3207fd89f2e2e1c5f1f21de8f9924707"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/74GYG5BXSCHC4MICCSJCV52FYY/bundle.json","state_url":"https://pith.science/pith/74GYG5BXSCHC4MICCSJCV52FYY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/74GYG5BXSCHC4MICCSJCV52FYY/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":"2026-08-11T10:36:54Z","links":{"resolver":"https://pith.science/pith/74GYG5BXSCHC4MICCSJCV52FYY","bundle":"https://pith.science/pith/74GYG5BXSCHC4MICCSJCV52FYY/bundle.json","state":"https://pith.science/pith/74GYG5BXSCHC4MICCSJCV52FYY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/74GYG5BXSCHC4MICCSJCV52FYY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:74GYG5BXSCHC4MICCSJCV52FYY","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":"95ea6517d5e09edbf3338a1018a91e1200f59d72bcb582abda8923df3b24771f","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2024-12-24T15:55:30Z","title_canon_sha256":"f850c9ac83605e79c797f7b0ef97ccb0910ae8c68cb4c711c7e22ad0a9497bfb"},"schema_version":"1.0","source":{"id":"2412.18518","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.18518","created_at":"2026-07-05T09:53:56Z"},{"alias_kind":"arxiv_version","alias_value":"2412.18518v1","created_at":"2026-07-05T09:53:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.18518","created_at":"2026-07-05T09:53:56Z"},{"alias_kind":"pith_short_12","alias_value":"74GYG5BXSCHC","created_at":"2026-07-05T09:53:56Z"},{"alias_kind":"pith_short_16","alias_value":"74GYG5BXSCHC4MIC","created_at":"2026-07-05T09:53:56Z"},{"alias_kind":"pith_short_8","alias_value":"74GYG5BX","created_at":"2026-07-05T09:53:56Z"}],"graph_snapshots":[{"event_id":"sha256:e693f3cae93b7b4068dcca4337d7d62e3207fd89f2e2e1c5f1f21de8f9924707","target":"graph","created_at":"2026-07-05T09:53:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.18518/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Bilevel optimization, a hierarchical mathematical framework where one optimization problem is nested within another, has emerged as a powerful tool for modeling complex decision-making processes in various fields such as economics, engineering, and machine learning. This paper focuses on bilevel optimization where both upper-level and lower-level functions are black boxes and expensive to evaluate. We propose a Bayesian Optimization framework that models the upper and lower-level functions as Gaussian processes over the combined space of upper and lower-level decisions, allowing us to exploit ","authors_text":"Juergen Branke, Nursen Aydin, Omer Ekmekcioglu","cross_cats":["math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2024-12-24T15:55:30Z","title":"Bayesian Optimization of Bilevel Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.18518","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:ab2e6384e2be00a04c60469fa7b39dc9da1018ed5def3a6071c3b8440eb28097","target":"record","created_at":"2026-07-05T09:53:56Z","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":"95ea6517d5e09edbf3338a1018a91e1200f59d72bcb582abda8923df3b24771f","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2024-12-24T15:55:30Z","title_canon_sha256":"f850c9ac83605e79c797f7b0ef97ccb0910ae8c68cb4c711c7e22ad0a9497bfb"},"schema_version":"1.0","source":{"id":"2412.18518","kind":"arxiv","version":1}},"canonical_sha256":"ff0d837437908e2e310214922af745c63fe371f709a704ea3ec024960cc97372","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff0d837437908e2e310214922af745c63fe371f709a704ea3ec024960cc97372","first_computed_at":"2026-07-05T09:53:56.932169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:53:56.932169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MhnIQ2LfXX3gUHDptB/VNoiU2lausvdIFc21dGwkRFNIbk7KEscTPGEEqkOzgGOkDNGkmVb8uL11DxXBW/5pBw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:53:56.932555Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.18518","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab2e6384e2be00a04c60469fa7b39dc9da1018ed5def3a6071c3b8440eb28097","sha256:e693f3cae93b7b4068dcca4337d7d62e3207fd89f2e2e1c5f1f21de8f9924707"],"state_sha256":"4276801c86ddfac5585108f95fc22c4b94cb40558a4e1bfc1c1ca7304af98c65"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UiHyPFGXZuU/vXvFHDMdy5SJHfIm2UKp8DyLCVHM3tdjtP37SmsCWb/S3vtXow6NEC0cNxhVWa/gGzvnN2hFDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T10:36:54.836682Z","bundle_sha256":"eeddd4a36d56ca3bebee5c7b1ec532eaf29221ab3bdb4030a780bdb69704b526"}}