{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:GT3JOTKWUBMGA5EVDWDAYZ5GCH","short_pith_number":"pith:GT3JOTKW","canonical_record":{"source":{"id":"2111.00552","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-10-31T17:46:26Z","cross_cats_sorted":["cs.AI","math.OC"],"title_canon_sha256":"c6f6f7f46225da5645238b63147b00b5d445600ca369bbd9ffe174a6a9ed005c","abstract_canon_sha256":"a582b72c4320af28d247386e8e8ec271d65dbc8fa83d7f14ade77668a4786007"},"schema_version":"1.0"},"canonical_sha256":"34f6974d56a0586074951d860c67a611d0381f68ec6d541ba8c3e0e579dace4b","source":{"kind":"arxiv","id":"2111.00552","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.00552","created_at":"2026-07-05T03:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"2111.00552v2","created_at":"2026-07-05T03:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.00552","created_at":"2026-07-05T03:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"GT3JOTKWUBMG","created_at":"2026-07-05T03:54:03Z"},{"alias_kind":"pith_short_16","alias_value":"GT3JOTKWUBMGA5EV","created_at":"2026-07-05T03:54:03Z"},{"alias_kind":"pith_short_8","alias_value":"GT3JOTKW","created_at":"2026-07-05T03:54:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:GT3JOTKWUBMGA5EVDWDAYZ5GCH","target":"record","payload":{"canonical_record":{"source":{"id":"2111.00552","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-10-31T17:46:26Z","cross_cats_sorted":["cs.AI","math.OC"],"title_canon_sha256":"c6f6f7f46225da5645238b63147b00b5d445600ca369bbd9ffe174a6a9ed005c","abstract_canon_sha256":"a582b72c4320af28d247386e8e8ec271d65dbc8fa83d7f14ade77668a4786007"},"schema_version":"1.0"},"canonical_sha256":"34f6974d56a0586074951d860c67a611d0381f68ec6d541ba8c3e0e579dace4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:54:03.354103Z","signature_b64":"1bje0IzsvIWfekPg2pizA25ilHc4Yuvgr+MdFDR5oyZORU8yJADsOrUVQnpZK49EbpCyoXQ6I/8FK/U/cp2/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34f6974d56a0586074951d860c67a611d0381f68ec6d541ba8c3e0e579dace4b","last_reissued_at":"2026-07-05T03:54:03.353688Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:54:03.353688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2111.00552","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:54:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HpmvjR1aH9kAvi2mXPrxEQX7oBEQ2kAOx1gTXqikAPl/Jstdje3I+dIV+0mpsXMiE7LfkuIJTziMl3ebp0kqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T19:17:48.124303Z"},"content_sha256":"e7b724c7869f0d51149f4a56ef56da45c79dc3bb8ed0bc3a716aeb4916e3b2c4","schema_version":"1.0","event_id":"sha256:e7b724c7869f0d51149f4a56ef56da45c79dc3bb8ed0bc3a716aeb4916e3b2c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:GT3JOTKWUBMGA5EVDWDAYZ5GCH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Policy Optimization for Constrained MDPs with Provable Fast Global Convergence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","math.OC"],"primary_cat":"cs.LG","authors_text":"Chao Tian, Dileep Kalathil, P. R. Kumar, Ruida Zhou, Tao Liu","submitted_at":"2021-10-31T17:46:26Z","abstract_excerpt":"We address the problem of finding the optimal policy of a constrained Markov decision process (CMDP) using a gradient descent-based algorithm. Previous results have shown that a primal-dual approach can achieve an $\\mathcal{O}(1/\\sqrt{T})$ global convergence rate for both the optimality gap and the constraint violation. We propose a new algorithm called policy mirror descent-primal dual (PMD-PD) algorithm that can provably achieve a faster $\\mathcal{O}(\\log(T)/T)$ convergence rate for both the optimality gap and the constraint violation. For the primal (policy) update, the PMD-PD algorithm uti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.00552","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/2111.00552/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":"2026-07-05T03:54:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NG7YG56CjKz+m5KYnRnMGGvLH15lhBJk+ufXQuZYX9V0qJBUWW87ysWFTaYQHd7n5LcgCJnBTLNKnWfFgQlfAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T19:17:48.124841Z"},"content_sha256":"ac0326c80bd9daf346d5a851b9583f8101710b6c479f04f1c90baf367715883f","schema_version":"1.0","event_id":"sha256:ac0326c80bd9daf346d5a851b9583f8101710b6c479f04f1c90baf367715883f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GT3JOTKWUBMGA5EVDWDAYZ5GCH/bundle.json","state_url":"https://pith.science/pith/GT3JOTKWUBMGA5EVDWDAYZ5GCH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GT3JOTKWUBMGA5EVDWDAYZ5GCH/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":"2026-08-08T19:17:48Z","links":{"resolver":"https://pith.science/pith/GT3JOTKWUBMGA5EVDWDAYZ5GCH","bundle":"https://pith.science/pith/GT3JOTKWUBMGA5EVDWDAYZ5GCH/bundle.json","state":"https://pith.science/pith/GT3JOTKWUBMGA5EVDWDAYZ5GCH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GT3JOTKWUBMGA5EVDWDAYZ5GCH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:GT3JOTKWUBMGA5EVDWDAYZ5GCH","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":"a582b72c4320af28d247386e8e8ec271d65dbc8fa83d7f14ade77668a4786007","cross_cats_sorted":["cs.AI","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-10-31T17:46:26Z","title_canon_sha256":"c6f6f7f46225da5645238b63147b00b5d445600ca369bbd9ffe174a6a9ed005c"},"schema_version":"1.0","source":{"id":"2111.00552","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.00552","created_at":"2026-07-05T03:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"2111.00552v2","created_at":"2026-07-05T03:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.00552","created_at":"2026-07-05T03:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"GT3JOTKWUBMG","created_at":"2026-07-05T03:54:03Z"},{"alias_kind":"pith_short_16","alias_value":"GT3JOTKWUBMGA5EV","created_at":"2026-07-05T03:54:03Z"},{"alias_kind":"pith_short_8","alias_value":"GT3JOTKW","created_at":"2026-07-05T03:54:03Z"}],"graph_snapshots":[{"event_id":"sha256:ac0326c80bd9daf346d5a851b9583f8101710b6c479f04f1c90baf367715883f","target":"graph","created_at":"2026-07-05T03:54:03Z","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/2111.00552/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We address the problem of finding the optimal policy of a constrained Markov decision process (CMDP) using a gradient descent-based algorithm. Previous results have shown that a primal-dual approach can achieve an $\\mathcal{O}(1/\\sqrt{T})$ global convergence rate for both the optimality gap and the constraint violation. We propose a new algorithm called policy mirror descent-primal dual (PMD-PD) algorithm that can provably achieve a faster $\\mathcal{O}(\\log(T)/T)$ convergence rate for both the optimality gap and the constraint violation. For the primal (policy) update, the PMD-PD algorithm uti","authors_text":"Chao Tian, Dileep Kalathil, P. R. Kumar, Ruida Zhou, Tao Liu","cross_cats":["cs.AI","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-10-31T17:46:26Z","title":"Policy Optimization for Constrained MDPs with Provable Fast Global Convergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.00552","kind":"arxiv","version":2},"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:e7b724c7869f0d51149f4a56ef56da45c79dc3bb8ed0bc3a716aeb4916e3b2c4","target":"record","created_at":"2026-07-05T03:54:03Z","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":"a582b72c4320af28d247386e8e8ec271d65dbc8fa83d7f14ade77668a4786007","cross_cats_sorted":["cs.AI","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-10-31T17:46:26Z","title_canon_sha256":"c6f6f7f46225da5645238b63147b00b5d445600ca369bbd9ffe174a6a9ed005c"},"schema_version":"1.0","source":{"id":"2111.00552","kind":"arxiv","version":2}},"canonical_sha256":"34f6974d56a0586074951d860c67a611d0381f68ec6d541ba8c3e0e579dace4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34f6974d56a0586074951d860c67a611d0381f68ec6d541ba8c3e0e579dace4b","first_computed_at":"2026-07-05T03:54:03.353688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:54:03.353688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1bje0IzsvIWfekPg2pizA25ilHc4Yuvgr+MdFDR5oyZORU8yJADsOrUVQnpZK49EbpCyoXQ6I/8FK/U/cp2/Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:54:03.354103Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.00552","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7b724c7869f0d51149f4a56ef56da45c79dc3bb8ed0bc3a716aeb4916e3b2c4","sha256:ac0326c80bd9daf346d5a851b9583f8101710b6c479f04f1c90baf367715883f"],"state_sha256":"b387010f49cbae75655c0349abe5399bd86b7beb25693a0ed3b5c2eaa0fe758f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s6fH8NvVJYoXOfIFYB247BVkd7U32x2lRx43oP7/UY5CQy4hs2MdOkGaQXOIzeXB9kH9nsmON7M1JD/JGzRwBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T19:17:48.130229Z","bundle_sha256":"0ffca8e5e6d42fb4ef51d08ef2e2a0f3152385c1580ead652312754ee50bd302"}}