{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LX4LLBMTKHLWRBEVHL5JDJ7KLF","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":"986660e74e1d7ae5a354bffa2f06d9da88f5ebe8567366c8afd0efae3a549af5","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-03-17T17:15:07Z","title_canon_sha256":"bb56fb9f01bf04d8e9332d1cddc7d525809694c8ccdefac5e72a78818b7ed300"},"schema_version":"1.0","source":{"id":"1403.4175","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4175","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4175v1","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4175","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"LX4LLBMTKHLW","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LX4LLBMTKHLWRBEV","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LX4LLBMT","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:bda367aa1e7a2cb136e8f7acf775d7afdbcf59658593f53edd56b30d12918314","target":"graph","created_at":"2026-05-18T02:56:12Z","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":"We develop a new Approximate Dynamic Programming (ADP) method for infinite horizon discounted reward Markov Decision Processes (MDP) based on projection onto a subsemimodule. We approximate the value function in terms of a $(\\min,+)$ linear combination of a set of basis functions whose $(\\min,+)$ linear span constitutes a subsemimodule. The projection operator is closely related to the Fenchel transform. Our approximate solution obeys the $(\\min,+)$ Projected Bellman Equation (MPPBE) which is different from the conventional Projected Bellman Equation (PBE). We show that the approximation error","authors_text":"Chandrashekar Lakshminarayanan, Shalabh Bhatnagar","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-03-17T17:15:07Z","title":"Approximate Dynamic Programming based on Projection onto the (min,+) subsemimodule"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4175","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":"sha256:25e892c785f5b78de7bbdf68057b107db408b587ece3201fe0334514e801df06","target":"record","created_at":"2026-05-18T02:56:12Z","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":"986660e74e1d7ae5a354bffa2f06d9da88f5ebe8567366c8afd0efae3a549af5","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-03-17T17:15:07Z","title_canon_sha256":"bb56fb9f01bf04d8e9332d1cddc7d525809694c8ccdefac5e72a78818b7ed300"},"schema_version":"1.0","source":{"id":"1403.4175","kind":"arxiv","version":1}},"canonical_sha256":"5df8b5859351d76884953afa91a7ea59404b286ae57ec576921328d0e817a6a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5df8b5859351d76884953afa91a7ea59404b286ae57ec576921328d0e817a6a1","first_computed_at":"2026-05-18T02:56:12.054696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:12.054696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/aBRaBkVfztxeBXgdY/rfp1hbnfVmct7hCQ4L/06ipc84oTFP0zOYhuQugTfEg0e1mFbepFh7Q/CthZ38AIACQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:12.055041Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.4175","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25e892c785f5b78de7bbdf68057b107db408b587ece3201fe0334514e801df06","sha256:bda367aa1e7a2cb136e8f7acf775d7afdbcf59658593f53edd56b30d12918314"],"state_sha256":"62e62b77c9f8bda0aa132880654a3b620fe529d7cf82f9d0c4d32c03f49041d5"}