{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:FQOHNSOIDIUWDYFQRNU7XKANGA","short_pith_number":"pith:FQOHNSOI","schema_version":"1.0","canonical_sha256":"2c1c76c9c81a2961e0b08b69fba80d300b9e74187381f088b179f5361bae7752","source":{"kind":"arxiv","id":"2010.04465","version":1},"attestation_state":"computed","paper":{"title":"Approximative Policy Iteration for Exit Time Feedback Control Problems driven by Stochastic Differential Equations using Tensor Train format","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Konstantin Fackeldey, Leon Sallandt, Mathias Oster, Reinhold Schneider","submitted_at":"2020-10-09T09:46:07Z","abstract_excerpt":"We consider a stochastic optimal exit time feedback control problem. The Bellman equation is solved approximatively via the Policy Iteration algorithm on a polynomial ansatz space by a sequence of linear equations. As high degree multi-polynomials are needed, the corresponding equations suffer from the curse of dimensionality even in moderate dimensions. We employ tensor-train methods to account for this problem. The approximation process within the Policy Iteration is done via a Least-Squares ansatz and the integration is done via Monte-Carlo methods. Numerical evidences are given for the (mu"},"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":"2010.04465","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-10-09T09:46:07Z","cross_cats_sorted":[],"title_canon_sha256":"082128ed975bb4f9b40ad34d6a07e3a2d80a5ce5070496667966fc10c8082081","abstract_canon_sha256":"b8337453e600a75c54ba32d18124c7f1f085e21440be10b7d5d2d0a95830d632"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:41:38.347461Z","signature_b64":"f4B0RpVlaDS5ZO78DuawOOQjEPZJSZUZFvKieuxovKaGyup19M6fjTXPvxW4K6+sJc/O/aDOznrY+sQdXlVVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c1c76c9c81a2961e0b08b69fba80d300b9e74187381f088b179f5361bae7752","last_reissued_at":"2026-07-05T01:41:38.346946Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:41:38.346946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximative Policy Iteration for Exit Time Feedback Control Problems driven by Stochastic Differential Equations using Tensor Train format","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Konstantin Fackeldey, Leon Sallandt, Mathias Oster, Reinhold Schneider","submitted_at":"2020-10-09T09:46:07Z","abstract_excerpt":"We consider a stochastic optimal exit time feedback control problem. The Bellman equation is solved approximatively via the Policy Iteration algorithm on a polynomial ansatz space by a sequence of linear equations. As high degree multi-polynomials are needed, the corresponding equations suffer from the curse of dimensionality even in moderate dimensions. We employ tensor-train methods to account for this problem. The approximation process within the Policy Iteration is done via a Least-Squares ansatz and the integration is done via Monte-Carlo methods. Numerical evidences are given for the (mu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.04465","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/2010.04465/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":"2010.04465","created_at":"2026-07-05T01:41:38.347009+00:00"},{"alias_kind":"arxiv_version","alias_value":"2010.04465v1","created_at":"2026-07-05T01:41:38.347009+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.04465","created_at":"2026-07-05T01:41:38.347009+00:00"},{"alias_kind":"pith_short_12","alias_value":"FQOHNSOIDIUW","created_at":"2026-07-05T01:41:38.347009+00:00"},{"alias_kind":"pith_short_16","alias_value":"FQOHNSOIDIUWDYFQ","created_at":"2026-07-05T01:41:38.347009+00:00"},{"alias_kind":"pith_short_8","alias_value":"FQOHNSOI","created_at":"2026-07-05T01:41:38.347009+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.30487","citing_title":"Discovering the Kalman-Bucy-Koopman Filter","ref_index":36,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FQOHNSOIDIUWDYFQRNU7XKANGA","json":"https://pith.science/pith/FQOHNSOIDIUWDYFQRNU7XKANGA.json","graph_json":"https://pith.science/api/pith-number/FQOHNSOIDIUWDYFQRNU7XKANGA/graph.json","events_json":"https://pith.science/api/pith-number/FQOHNSOIDIUWDYFQRNU7XKANGA/events.json","paper":"https://pith.science/paper/FQOHNSOI"},"agent_actions":{"view_html":"https://pith.science/pith/FQOHNSOIDIUWDYFQRNU7XKANGA","download_json":"https://pith.science/pith/FQOHNSOIDIUWDYFQRNU7XKANGA.json","view_paper":"https://pith.science/paper/FQOHNSOI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2010.04465&json=true","fetch_graph":"https://pith.science/api/pith-number/FQOHNSOIDIUWDYFQRNU7XKANGA/graph.json","fetch_events":"https://pith.science/api/pith-number/FQOHNSOIDIUWDYFQRNU7XKANGA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FQOHNSOIDIUWDYFQRNU7XKANGA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FQOHNSOIDIUWDYFQRNU7XKANGA/action/storage_attestation","attest_author":"https://pith.science/pith/FQOHNSOIDIUWDYFQRNU7XKANGA/action/author_attestation","sign_citation":"https://pith.science/pith/FQOHNSOIDIUWDYFQRNU7XKANGA/action/citation_signature","submit_replication":"https://pith.science/pith/FQOHNSOIDIUWDYFQRNU7XKANGA/action/replication_record"}},"created_at":"2026-07-05T01:41:38.347009+00:00","updated_at":"2026-07-05T01:41:38.347009+00:00"}