{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:XHQZHYRL7MWMPRDNVS7IIKLSI2","short_pith_number":"pith:XHQZHYRL","canonical_record":{"source":{"id":"2502.07764","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2025-02-11T18:47:53Z","cross_cats_sorted":["cs.AI","cs.LG"],"title_canon_sha256":"fefb2463a2977a050bc0997903aca63b82fea6a965baa5db0d64713d44be3129","abstract_canon_sha256":"9ef94554edc59f98075dba844feec96ffcc7726e388a0f9e42948109704eabb4"},"schema_version":"1.0"},"canonical_sha256":"b9e193e22bfb2cc7c46dacbe84297246b057176aab31937d16f2e41690009154","source":{"kind":"arxiv","id":"2502.07764","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.07764","created_at":"2026-07-05T10:12:53Z"},{"alias_kind":"arxiv_version","alias_value":"2502.07764v1","created_at":"2026-07-05T10:12:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.07764","created_at":"2026-07-05T10:12:53Z"},{"alias_kind":"pith_short_12","alias_value":"XHQZHYRL7MWM","created_at":"2026-07-05T10:12:53Z"},{"alias_kind":"pith_short_16","alias_value":"XHQZHYRL7MWMPRDN","created_at":"2026-07-05T10:12:53Z"},{"alias_kind":"pith_short_8","alias_value":"XHQZHYRL","created_at":"2026-07-05T10:12:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:XHQZHYRL7MWMPRDNVS7IIKLSI2","target":"record","payload":{"canonical_record":{"source":{"id":"2502.07764","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2025-02-11T18:47:53Z","cross_cats_sorted":["cs.AI","cs.LG"],"title_canon_sha256":"fefb2463a2977a050bc0997903aca63b82fea6a965baa5db0d64713d44be3129","abstract_canon_sha256":"9ef94554edc59f98075dba844feec96ffcc7726e388a0f9e42948109704eabb4"},"schema_version":"1.0"},"canonical_sha256":"b9e193e22bfb2cc7c46dacbe84297246b057176aab31937d16f2e41690009154","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:12:53.594635Z","signature_b64":"87+WJE9dwLM2y7swdOtXrFgOPf4nptzSFTIA3rZlrDFjOL6830vaCjj6I7xmdQ67OJ0tN+5ZvHcw9bqi2MvNBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9e193e22bfb2cc7c46dacbe84297246b057176aab31937d16f2e41690009154","last_reissued_at":"2026-07-05T10:12:53.594138Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:12:53.594138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.07764","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":"2026-07-05T10:12:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uGomw34eGEv22I3YcSIBv/JwogNoPX65XxESVbVFBIMn4uGQTz+dhA3pYSMliLrBRircMDJytfc5YzILcDznDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T23:04:58.519651Z"},"content_sha256":"4298e0aef1fb2a3b045e4879ff819d804e545da019b4e04a743e7c75a643db2a","schema_version":"1.0","event_id":"sha256:4298e0aef1fb2a3b045e4879ff819d804e545da019b4e04a743e7c75a643db2a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:XHQZHYRL7MWMPRDNVS7IIKLSI2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial-Time Approximability of Constrained Reinforcement Learning","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.AI","cs.LG"],"primary_cat":"cs.DS","authors_text":"Jeremy McMahan","submitted_at":"2025-02-11T18:47:53Z","abstract_excerpt":"We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\\epsilon)$-additive bicriteria approximation algorithm for finding optimal constrained policies across a broad class of recursively computable constraints, including almost-sure, chance, expectation, and their anytime variants. Matching lower bounds imply our approximation guarantees are optimal so long as $P \\neq NP$. The generality of our approach results in answers to several long-standing open complexity questions in the const"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07764","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/2502.07764/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":"2026-07-05T10:12:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cGzexE9CC3Dt0awTkjHfXv23hQp/xPXtVfn8kGmqPP8zUzTnUBCRa8j4XMmnLG4JG5g10ZZd8QelwTBOzv6kDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T23:04:58.520246Z"},"content_sha256":"600d86dd4868a87e18b3918adc907b85a22838e8d360ddf9cc45a50e1e0519ff","schema_version":"1.0","event_id":"sha256:600d86dd4868a87e18b3918adc907b85a22838e8d360ddf9cc45a50e1e0519ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XHQZHYRL7MWMPRDNVS7IIKLSI2/bundle.json","state_url":"https://pith.science/pith/XHQZHYRL7MWMPRDNVS7IIKLSI2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XHQZHYRL7MWMPRDNVS7IIKLSI2/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":"2026-08-08T23:04:58Z","links":{"resolver":"https://pith.science/pith/XHQZHYRL7MWMPRDNVS7IIKLSI2","bundle":"https://pith.science/pith/XHQZHYRL7MWMPRDNVS7IIKLSI2/bundle.json","state":"https://pith.science/pith/XHQZHYRL7MWMPRDNVS7IIKLSI2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XHQZHYRL7MWMPRDNVS7IIKLSI2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XHQZHYRL7MWMPRDNVS7IIKLSI2","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":"9ef94554edc59f98075dba844feec96ffcc7726e388a0f9e42948109704eabb4","cross_cats_sorted":["cs.AI","cs.LG"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2025-02-11T18:47:53Z","title_canon_sha256":"fefb2463a2977a050bc0997903aca63b82fea6a965baa5db0d64713d44be3129"},"schema_version":"1.0","source":{"id":"2502.07764","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.07764","created_at":"2026-07-05T10:12:53Z"},{"alias_kind":"arxiv_version","alias_value":"2502.07764v1","created_at":"2026-07-05T10:12:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.07764","created_at":"2026-07-05T10:12:53Z"},{"alias_kind":"pith_short_12","alias_value":"XHQZHYRL7MWM","created_at":"2026-07-05T10:12:53Z"},{"alias_kind":"pith_short_16","alias_value":"XHQZHYRL7MWMPRDN","created_at":"2026-07-05T10:12:53Z"},{"alias_kind":"pith_short_8","alias_value":"XHQZHYRL","created_at":"2026-07-05T10:12:53Z"}],"graph_snapshots":[{"event_id":"sha256:600d86dd4868a87e18b3918adc907b85a22838e8d360ddf9cc45a50e1e0519ff","target":"graph","created_at":"2026-07-05T10:12:53Z","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/2502.07764/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\\epsilon)$-additive bicriteria approximation algorithm for finding optimal constrained policies across a broad class of recursively computable constraints, including almost-sure, chance, expectation, and their anytime variants. Matching lower bounds imply our approximation guarantees are optimal so long as $P \\neq NP$. The generality of our approach results in answers to several long-standing open complexity questions in the const","authors_text":"Jeremy McMahan","cross_cats":["cs.AI","cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2025-02-11T18:47:53Z","title":"Polynomial-Time Approximability of Constrained Reinforcement Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07764","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":"sha256:4298e0aef1fb2a3b045e4879ff819d804e545da019b4e04a743e7c75a643db2a","target":"record","created_at":"2026-07-05T10:12:53Z","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":"9ef94554edc59f98075dba844feec96ffcc7726e388a0f9e42948109704eabb4","cross_cats_sorted":["cs.AI","cs.LG"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2025-02-11T18:47:53Z","title_canon_sha256":"fefb2463a2977a050bc0997903aca63b82fea6a965baa5db0d64713d44be3129"},"schema_version":"1.0","source":{"id":"2502.07764","kind":"arxiv","version":1}},"canonical_sha256":"b9e193e22bfb2cc7c46dacbe84297246b057176aab31937d16f2e41690009154","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9e193e22bfb2cc7c46dacbe84297246b057176aab31937d16f2e41690009154","first_computed_at":"2026-07-05T10:12:53.594138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:12:53.594138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"87+WJE9dwLM2y7swdOtXrFgOPf4nptzSFTIA3rZlrDFjOL6830vaCjj6I7xmdQ67OJ0tN+5ZvHcw9bqi2MvNBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:12:53.594635Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.07764","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4298e0aef1fb2a3b045e4879ff819d804e545da019b4e04a743e7c75a643db2a","sha256:600d86dd4868a87e18b3918adc907b85a22838e8d360ddf9cc45a50e1e0519ff"],"state_sha256":"de6a352f8a7f5e9a8a3a476c407d71e4c2d9fa320a5d8b835dff25551aca82cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XyjUFfyUvA57tIYfF7K6qG1vukUUe0nQc5dwEPXG2MW178UpA7VuVB8BbGJCdT9oyjCOpNDPbnJhJAFCGTy2Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T23:04:58.525092Z","bundle_sha256":"f7de1604b48d8cfad50ba3c52f139bda57d1d0ad74d62f7feb2ed42ec989c6fd"}}