{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:ZNPWSB5YKXIVEVDC2ISR5VREEI","short_pith_number":"pith:ZNPWSB5Y","schema_version":"1.0","canonical_sha256":"cb5f6907b855d1525462d2251ed624221b3a5a99fd42fb31c2ea5661de9501d9","source":{"kind":"arxiv","id":"2201.11157","version":2},"attestation_state":"computed","paper":{"title":"Policy Optimization over Submanifolds for Linearly Constrained Feedback Synthesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","eess.SY","math.DG"],"primary_cat":"math.OC","authors_text":"Mehran Mesbahi, Shahriar Talebi","submitted_at":"2022-01-26T19:45:04Z","abstract_excerpt":"In this paper, we study linearly constrained policy optimization over the manifold of Schur stabilizing controllers, equipped with a Riemannian metric that emerges naturally in the context of optimal control problems. We provide extrinsic analysis of a generic constrained smooth cost function, that subsequently facilitates subsuming any such constrained problem into this framework. By studying the second order geometry of this manifold, we provide a Newton-type algorithm that does not rely on the exponential mapping nor a retraction, while ensuring local convergence guarantees. The algorithm h"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2201.11157","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-01-26T19:45:04Z","cross_cats_sorted":["cs.SY","eess.SY","math.DG"],"title_canon_sha256":"96c07983c9a0c13b2e784f9bd97b0983adc827fe6e9c67a36675851bff762934","abstract_canon_sha256":"0de8b2ab4a5e6dac72bc5128b3dbd3e575709ee297714d9fdc86a3e0b7b2fdc1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:05:29.304634Z","signature_b64":"0r9J5ndmfCfuGR+aEot4XycnL93uqSzzgi3ShRaLkzr14ydpphjHGQrPST5G61/IE3DDaCdi9rNWVnUAoFliDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb5f6907b855d1525462d2251ed624221b3a5a99fd42fb31c2ea5661de9501d9","last_reissued_at":"2026-07-05T07:05:29.304053Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:05:29.304053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Policy Optimization over Submanifolds for Linearly Constrained Feedback Synthesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","eess.SY","math.DG"],"primary_cat":"math.OC","authors_text":"Mehran Mesbahi, Shahriar Talebi","submitted_at":"2022-01-26T19:45:04Z","abstract_excerpt":"In this paper, we study linearly constrained policy optimization over the manifold of Schur stabilizing controllers, equipped with a Riemannian metric that emerges naturally in the context of optimal control problems. We provide extrinsic analysis of a generic constrained smooth cost function, that subsequently facilitates subsuming any such constrained problem into this framework. By studying the second order geometry of this manifold, we provide a Newton-type algorithm that does not rely on the exponential mapping nor a retraction, while ensuring local convergence guarantees. The algorithm h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.11157","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/2201.11157/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2201.11157","created_at":"2026-07-05T07:05:29.304115+00:00"},{"alias_kind":"arxiv_version","alias_value":"2201.11157v2","created_at":"2026-07-05T07:05:29.304115+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.11157","created_at":"2026-07-05T07:05:29.304115+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZNPWSB5YKXIV","created_at":"2026-07-05T07:05:29.304115+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZNPWSB5YKXIVEVDC","created_at":"2026-07-05T07:05:29.304115+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZNPWSB5Y","created_at":"2026-07-05T07:05:29.304115+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.05071","citing_title":"Learning Kalman Policy for Singular Unknown Covariances via Riemannian Regularization","ref_index":28,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZNPWSB5YKXIVEVDC2ISR5VREEI","json":"https://pith.science/pith/ZNPWSB5YKXIVEVDC2ISR5VREEI.json","graph_json":"https://pith.science/api/pith-number/ZNPWSB5YKXIVEVDC2ISR5VREEI/graph.json","events_json":"https://pith.science/api/pith-number/ZNPWSB5YKXIVEVDC2ISR5VREEI/events.json","paper":"https://pith.science/paper/ZNPWSB5Y"},"agent_actions":{"view_html":"https://pith.science/pith/ZNPWSB5YKXIVEVDC2ISR5VREEI","download_json":"https://pith.science/pith/ZNPWSB5YKXIVEVDC2ISR5VREEI.json","view_paper":"https://pith.science/paper/ZNPWSB5Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2201.11157&json=true","fetch_graph":"https://pith.science/api/pith-number/ZNPWSB5YKXIVEVDC2ISR5VREEI/graph.json","fetch_events":"https://pith.science/api/pith-number/ZNPWSB5YKXIVEVDC2ISR5VREEI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZNPWSB5YKXIVEVDC2ISR5VREEI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZNPWSB5YKXIVEVDC2ISR5VREEI/action/storage_attestation","attest_author":"https://pith.science/pith/ZNPWSB5YKXIVEVDC2ISR5VREEI/action/author_attestation","sign_citation":"https://pith.science/pith/ZNPWSB5YKXIVEVDC2ISR5VREEI/action/citation_signature","submit_replication":"https://pith.science/pith/ZNPWSB5YKXIVEVDC2ISR5VREEI/action/replication_record"}},"created_at":"2026-07-05T07:05:29.304115+00:00","updated_at":"2026-07-05T07:05:29.304115+00:00"}