{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:QKFWQBCLDB3YV7SX3DREPZRSRS","short_pith_number":"pith:QKFWQBCL","canonical_record":{"source":{"id":"2201.07443","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-01-19T07:03:37Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"98bc8e4148696a4ac456e6e9a37457fc6470ec2f8779aa5ce7f7f151c62c5040","abstract_canon_sha256":"99862981505870f14611e61bc17798857896bac669a7bd8d327fff89d7b477cb"},"schema_version":"1.0"},"canonical_sha256":"828b68044b18778afe57d8e247e6328c9394f2c1e21ab511d6ebd3e3ff4a1bb2","source":{"kind":"arxiv","id":"2201.07443","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.07443","created_at":"2026-07-05T04:02:22Z"},{"alias_kind":"arxiv_version","alias_value":"2201.07443v2","created_at":"2026-07-05T04:02:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.07443","created_at":"2026-07-05T04:02:22Z"},{"alias_kind":"pith_short_12","alias_value":"QKFWQBCLDB3Y","created_at":"2026-07-05T04:02:22Z"},{"alias_kind":"pith_short_16","alias_value":"QKFWQBCLDB3YV7SX","created_at":"2026-07-05T04:02:22Z"},{"alias_kind":"pith_short_8","alias_value":"QKFWQBCL","created_at":"2026-07-05T04:02:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:QKFWQBCLDB3YV7SX3DREPZRSRS","target":"record","payload":{"canonical_record":{"source":{"id":"2201.07443","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-01-19T07:03:37Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"98bc8e4148696a4ac456e6e9a37457fc6470ec2f8779aa5ce7f7f151c62c5040","abstract_canon_sha256":"99862981505870f14611e61bc17798857896bac669a7bd8d327fff89d7b477cb"},"schema_version":"1.0"},"canonical_sha256":"828b68044b18778afe57d8e247e6328c9394f2c1e21ab511d6ebd3e3ff4a1bb2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:02:22.631244Z","signature_b64":"knBrtJRNGd81NEhl3udd+5upfGvs2hwXfUcP9NXRQPe5HwB7jl8J8yFj9WLCOxgqpxZ8IbSZhrz6vC3+8RLNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"828b68044b18778afe57d8e247e6328c9394f2c1e21ab511d6ebd3e3ff4a1bb2","last_reissued_at":"2026-07-05T04:02:22.630813Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:02:22.630813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2201.07443","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":"2026-07-05T04:02:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9IMLYCOnjrIMEK0HefE/1jvsz9zr+ZwKQUUokQPJaGbZq4Amm4emAjbDw6UZ54gttRpJbTEDfCDNhZoi1IzYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T16:46:16.165630Z"},"content_sha256":"e966445ace6b54c5c10fe0334b1e9375585523bcb29921a6ba94e0de204e5a1f","schema_version":"1.0","event_id":"sha256:e966445ace6b54c5c10fe0334b1e9375585523bcb29921a6ba94e0de204e5a1f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:QKFWQBCLDB3YV7SX3DREPZRSRS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Convergence Rates of Policy Gradient Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Lin Xiao","submitted_at":"2022-01-19T07:03:37Z","abstract_excerpt":"We consider infinite-horizon discounted Markov decision problems with finite state and action spaces and study the convergence rates of the projected policy gradient method and a general class of policy mirror descent methods, all with direct parametrization in the policy space. First, we develop a theory of weak gradient-mapping dominance and use it to prove sharper sublinear convergence rate of the projected policy gradient method. Then we show that with geometrically increasing step sizes, a general class of policy mirror descent methods, including the natural policy gradient method and a p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.07443","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/2201.07443/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":"2026-07-05T04:02:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JrAZ+KQ0MNPqHpk4lSnC6bPyrmdZswWKGA5jUMD9rSJgvTCam9KA7NExkfl0w8Chb0Yr9pH5RifZSdM4eP8cCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T16:46:16.166640Z"},"content_sha256":"9e0d2cd73a42136186e432fc7820b24f0b4f76607913381b22e719ab22279ce9","schema_version":"1.0","event_id":"sha256:9e0d2cd73a42136186e432fc7820b24f0b4f76607913381b22e719ab22279ce9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QKFWQBCLDB3YV7SX3DREPZRSRS/bundle.json","state_url":"https://pith.science/pith/QKFWQBCLDB3YV7SX3DREPZRSRS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QKFWQBCLDB3YV7SX3DREPZRSRS/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":"2026-08-21T16:46:16Z","links":{"resolver":"https://pith.science/pith/QKFWQBCLDB3YV7SX3DREPZRSRS","bundle":"https://pith.science/pith/QKFWQBCLDB3YV7SX3DREPZRSRS/bundle.json","state":"https://pith.science/pith/QKFWQBCLDB3YV7SX3DREPZRSRS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QKFWQBCLDB3YV7SX3DREPZRSRS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:QKFWQBCLDB3YV7SX3DREPZRSRS","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":"99862981505870f14611e61bc17798857896bac669a7bd8d327fff89d7b477cb","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-01-19T07:03:37Z","title_canon_sha256":"98bc8e4148696a4ac456e6e9a37457fc6470ec2f8779aa5ce7f7f151c62c5040"},"schema_version":"1.0","source":{"id":"2201.07443","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.07443","created_at":"2026-07-05T04:02:22Z"},{"alias_kind":"arxiv_version","alias_value":"2201.07443v2","created_at":"2026-07-05T04:02:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.07443","created_at":"2026-07-05T04:02:22Z"},{"alias_kind":"pith_short_12","alias_value":"QKFWQBCLDB3Y","created_at":"2026-07-05T04:02:22Z"},{"alias_kind":"pith_short_16","alias_value":"QKFWQBCLDB3YV7SX","created_at":"2026-07-05T04:02:22Z"},{"alias_kind":"pith_short_8","alias_value":"QKFWQBCL","created_at":"2026-07-05T04:02:22Z"}],"graph_snapshots":[{"event_id":"sha256:9e0d2cd73a42136186e432fc7820b24f0b4f76607913381b22e719ab22279ce9","target":"graph","created_at":"2026-07-05T04:02:22Z","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/2201.07443/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider infinite-horizon discounted Markov decision problems with finite state and action spaces and study the convergence rates of the projected policy gradient method and a general class of policy mirror descent methods, all with direct parametrization in the policy space. First, we develop a theory of weak gradient-mapping dominance and use it to prove sharper sublinear convergence rate of the projected policy gradient method. Then we show that with geometrically increasing step sizes, a general class of policy mirror descent methods, including the natural policy gradient method and a p","authors_text":"Lin Xiao","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-01-19T07:03:37Z","title":"On the Convergence Rates of Policy Gradient Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.07443","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:e966445ace6b54c5c10fe0334b1e9375585523bcb29921a6ba94e0de204e5a1f","target":"record","created_at":"2026-07-05T04:02:22Z","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":"99862981505870f14611e61bc17798857896bac669a7bd8d327fff89d7b477cb","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-01-19T07:03:37Z","title_canon_sha256":"98bc8e4148696a4ac456e6e9a37457fc6470ec2f8779aa5ce7f7f151c62c5040"},"schema_version":"1.0","source":{"id":"2201.07443","kind":"arxiv","version":2}},"canonical_sha256":"828b68044b18778afe57d8e247e6328c9394f2c1e21ab511d6ebd3e3ff4a1bb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"828b68044b18778afe57d8e247e6328c9394f2c1e21ab511d6ebd3e3ff4a1bb2","first_computed_at":"2026-07-05T04:02:22.630813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:02:22.630813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"knBrtJRNGd81NEhl3udd+5upfGvs2hwXfUcP9NXRQPe5HwB7jl8J8yFj9WLCOxgqpxZ8IbSZhrz6vC3+8RLNDw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:02:22.631244Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.07443","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e966445ace6b54c5c10fe0334b1e9375585523bcb29921a6ba94e0de204e5a1f","sha256:9e0d2cd73a42136186e432fc7820b24f0b4f76607913381b22e719ab22279ce9"],"state_sha256":"36334c39e816235db39ae82a7ad914f9edd761659770ad0dc474c8f5a015f588"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iGC/GzLrx6MIk9O7slzR3sLBKz0ayOH4RftRP7TIUbZJxfIWO5OZHGg/d+7K2sbINGE8WxNICRbSFCIPrsN3BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T16:46:16.173210Z","bundle_sha256":"c1ef866bb96aeb7b7c13c84c5924b3f324b0f8f48495f9a0afcbf00257245ca7"}}