{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LGQ3EOLHXCWYMGQQ7XO454PUTO","short_pith_number":"pith:LGQ3EOLH","canonical_record":{"source":{"id":"1609.06331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-18T20:45:16Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"a2e92bcfcef19726fc673e345fcc41fc7926da38de2a94cdcafc49e4a29fd537","abstract_canon_sha256":"c0dc04d26bad784d2d929e5801df725d93f561b5bbf77b70907165a5dbf4f499"},"schema_version":"1.0"},"canonical_sha256":"59a1b23967b8ad861a10fdddcef1f49bbf15529ec705957a5681fc43e03917c0","source":{"kind":"arxiv","id":"1609.06331","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06331","created_at":"2026-05-18T01:04:08Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06331v1","created_at":"2026-05-18T01:04:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06331","created_at":"2026-05-18T01:04:08Z"},{"alias_kind":"pith_short_12","alias_value":"LGQ3EOLHXCWY","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LGQ3EOLHXCWYMGQQ","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LGQ3EOLH","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LGQ3EOLHXCWYMGQQ7XO454PUTO","target":"record","payload":{"canonical_record":{"source":{"id":"1609.06331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-18T20:45:16Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"a2e92bcfcef19726fc673e345fcc41fc7926da38de2a94cdcafc49e4a29fd537","abstract_canon_sha256":"c0dc04d26bad784d2d929e5801df725d93f561b5bbf77b70907165a5dbf4f499"},"schema_version":"1.0"},"canonical_sha256":"59a1b23967b8ad861a10fdddcef1f49bbf15529ec705957a5681fc43e03917c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:08.579779Z","signature_b64":"Fs2z1OP/N2HECGDrL313rFmMB9RRts7uZPBSfAqaOO4+Yn9TZs8J3huFyIZjOSXY0XbaZvdGEFKXbcaswoz6CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59a1b23967b8ad861a10fdddcef1f49bbf15529ec705957a5681fc43e03917c0","last_reissued_at":"2026-05-18T01:04:08.579010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:08.579010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.06331","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":"2026-05-18T01:04:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xW6YOesRhOow0yblwHRAT7KnAmOunLCwHAHWuzjiI/9PtGhhpoyji6RwYGpQ5fAiGX0QN2u8y4LwsorEphB/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:13:50.672456Z"},"content_sha256":"6d3b3a12b6f4795c481728639e0e498ba6625a33d4ccb07e65a44b3c89a9fa13","schema_version":"1.0","event_id":"sha256:6d3b3a12b6f4795c481728639e0e498ba6625a33d4ccb07e65a44b3c89a9fa13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LGQ3EOLHXCWYMGQQ7XO454PUTO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Max-affine estimators for convex stochastic programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"math.OC","authors_text":"Andr\\'as Gy\\\"orgy, Csaba Szepesv\\'ari, G\\'abor Bal\\'azs","submitted_at":"2016-09-18T20:45:16Z","abstract_excerpt":"In this paper, we consider two sequential decision making problems with a convexity structure, namely an energy storage optimization task and a multi-product assembly example. We formulate these problems in the stochastic programming framework and discuss an approximate dynamic programming technique for their solutions. As the cost-to-go functions are convex in these cases, we use max-affine estimates for their approximations. To train such a max-affine estimate, we provide a new convex regression algorithm, and evaluate it empirically for these planning scenarios."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06331","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":"2026-05-18T01:04:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"toya5ywjw9NyvcfobG3KrFti4Lc/DKMAthbOEkf2FhsUFdkiK9i8+1bAJ2XjDn0prG70KjjbNE5QxKc8OetoAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:13:50.673139Z"},"content_sha256":"66b3848a7b07b3fbb95171d9e29712e20db84f55ea10be2d40e2eb9eff9d144f","schema_version":"1.0","event_id":"sha256:66b3848a7b07b3fbb95171d9e29712e20db84f55ea10be2d40e2eb9eff9d144f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LGQ3EOLHXCWYMGQQ7XO454PUTO/bundle.json","state_url":"https://pith.science/pith/LGQ3EOLHXCWYMGQQ7XO454PUTO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LGQ3EOLHXCWYMGQQ7XO454PUTO/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":"2026-06-07T22:13:50Z","links":{"resolver":"https://pith.science/pith/LGQ3EOLHXCWYMGQQ7XO454PUTO","bundle":"https://pith.science/pith/LGQ3EOLHXCWYMGQQ7XO454PUTO/bundle.json","state":"https://pith.science/pith/LGQ3EOLHXCWYMGQQ7XO454PUTO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LGQ3EOLHXCWYMGQQ7XO454PUTO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LGQ3EOLHXCWYMGQQ7XO454PUTO","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":"c0dc04d26bad784d2d929e5801df725d93f561b5bbf77b70907165a5dbf4f499","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-18T20:45:16Z","title_canon_sha256":"a2e92bcfcef19726fc673e345fcc41fc7926da38de2a94cdcafc49e4a29fd537"},"schema_version":"1.0","source":{"id":"1609.06331","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06331","created_at":"2026-05-18T01:04:08Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06331v1","created_at":"2026-05-18T01:04:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06331","created_at":"2026-05-18T01:04:08Z"},{"alias_kind":"pith_short_12","alias_value":"LGQ3EOLHXCWY","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LGQ3EOLHXCWYMGQQ","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LGQ3EOLH","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:66b3848a7b07b3fbb95171d9e29712e20db84f55ea10be2d40e2eb9eff9d144f","target":"graph","created_at":"2026-05-18T01:04:08Z","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":"In this paper, we consider two sequential decision making problems with a convexity structure, namely an energy storage optimization task and a multi-product assembly example. We formulate these problems in the stochastic programming framework and discuss an approximate dynamic programming technique for their solutions. As the cost-to-go functions are convex in these cases, we use max-affine estimates for their approximations. To train such a max-affine estimate, we provide a new convex regression algorithm, and evaluate it empirically for these planning scenarios.","authors_text":"Andr\\'as Gy\\\"orgy, Csaba Szepesv\\'ari, G\\'abor Bal\\'azs","cross_cats":["cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-18T20:45:16Z","title":"Max-affine estimators for convex stochastic programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06331","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":"sha256:6d3b3a12b6f4795c481728639e0e498ba6625a33d4ccb07e65a44b3c89a9fa13","target":"record","created_at":"2026-05-18T01:04:08Z","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":"c0dc04d26bad784d2d929e5801df725d93f561b5bbf77b70907165a5dbf4f499","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-18T20:45:16Z","title_canon_sha256":"a2e92bcfcef19726fc673e345fcc41fc7926da38de2a94cdcafc49e4a29fd537"},"schema_version":"1.0","source":{"id":"1609.06331","kind":"arxiv","version":1}},"canonical_sha256":"59a1b23967b8ad861a10fdddcef1f49bbf15529ec705957a5681fc43e03917c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59a1b23967b8ad861a10fdddcef1f49bbf15529ec705957a5681fc43e03917c0","first_computed_at":"2026-05-18T01:04:08.579010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:08.579010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fs2z1OP/N2HECGDrL313rFmMB9RRts7uZPBSfAqaOO4+Yn9TZs8J3huFyIZjOSXY0XbaZvdGEFKXbcaswoz6CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:08.579779Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.06331","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d3b3a12b6f4795c481728639e0e498ba6625a33d4ccb07e65a44b3c89a9fa13","sha256:66b3848a7b07b3fbb95171d9e29712e20db84f55ea10be2d40e2eb9eff9d144f"],"state_sha256":"30e69bc09dd3d9e9ddc0ae0014ee3c7fc4a9a273c41ab6f5bfba510fa3259877"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ok0HmGndHJLjH5IxofIbJ85twLsvUXZ8ji23LxLb2oVpRSmKdgyYX3oQZ+0yWExV46ahW8rcNYsA7Sx6b8+rAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T22:13:50.676575Z","bundle_sha256":"73ea2d83e234b50fb0334810ce18861591a58aa311246a2e416339a648688ed3"}}