{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:RT4SHFKY6ZYSFLXMQLBTZ77747","short_pith_number":"pith:RT4SHFKY","canonical_record":{"source":{"id":"2401.00364","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-12-31T01:30:14Z","cross_cats_sorted":["cs.SY","eess.SY","math.OC"],"title_canon_sha256":"b78e4cba94de92876da5d48b521b9d4f2cbed59016e399ba1021191abc320e10","abstract_canon_sha256":"7d980dc64112393594469d08efecba0e16c45cd6956bf985d03d7e73daf0f169"},"schema_version":"1.0"},"canonical_sha256":"8cf9239558f67122aeec82c33cffffe7e00d678288d7ce3e71df1a107f5b5418","source":{"kind":"arxiv","id":"2401.00364","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.00364","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"arxiv_version","alias_value":"2401.00364v2","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.00364","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"pith_short_12","alias_value":"RT4SHFKY6ZYS","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"pith_short_16","alias_value":"RT4SHFKY6ZYSFLXM","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"pith_short_8","alias_value":"RT4SHFKY","created_at":"2026-07-05T11:01:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:RT4SHFKY6ZYSFLXMQLBTZ77747","target":"record","payload":{"canonical_record":{"source":{"id":"2401.00364","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-12-31T01:30:14Z","cross_cats_sorted":["cs.SY","eess.SY","math.OC"],"title_canon_sha256":"b78e4cba94de92876da5d48b521b9d4f2cbed59016e399ba1021191abc320e10","abstract_canon_sha256":"7d980dc64112393594469d08efecba0e16c45cd6956bf985d03d7e73daf0f169"},"schema_version":"1.0"},"canonical_sha256":"8cf9239558f67122aeec82c33cffffe7e00d678288d7ce3e71df1a107f5b5418","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:01:22.837892Z","signature_b64":"AJyhBUwSFMg+LJGpB4PTD8YnS0beyclth/Rj7Y681LhZolxOMUemb1xp9ou9yqP866FPVsrytEIoKK+RQIIVAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cf9239558f67122aeec82c33cffffe7e00d678288d7ce3e71df1a107f5b5418","last_reissued_at":"2026-07-05T11:01:22.837360Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:01:22.837360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.00364","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":"2026-07-05T11:01:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fhRoX33BFOf1p/lkUWHF5SinjuXrjj5ETZp7DyCESQkXYrsc0h5/qLZaj0tfZv0nxHSEfDB/v1E6fiFZ9wXDBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T16:55:56.531897Z"},"content_sha256":"b1db6ee2feb2ccef7bf4b807c9eb21eb64bdaf3ad7ba9f1777610889bd20801c","schema_version":"1.0","event_id":"sha256:b1db6ee2feb2ccef7bf4b807c9eb21eb64bdaf3ad7ba9f1777610889bd20801c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:RT4SHFKY6ZYSFLXMQLBTZ77747","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tight Finite Time Bounds of Two-Time-Scale Linear Stochastic Approximation with Markovian Noise","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SY","eess.SY","math.OC"],"primary_cat":"cs.LG","authors_text":"Sajad Khodadadian, Shaan Ul Haque, Siva Theja Maguluri","submitted_at":"2023-12-31T01:30:14Z","abstract_excerpt":"Stochastic approximation (SA) is an iterative algorithm for finding the fixed point of an operator using noisy samples and widely used in optimization and Reinforcement Learning (RL). The noise in RL exhibits a Markovian structure, and in some cases, such as gradient temporal difference (GTD) methods, SA is employed in a two-time-scale framework. This combination introduces significant theoretical challenges for analysis.\n  We derive an upper bound on the error for the iterations of linear two-time-scale SA with Markovian noise. We demonstrate that the mean squared error decreases as $trace (\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.00364","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/2401.00364/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":"2026-07-05T11:01:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/TiGImuq152Xkc91YmomaH32HExPeifycCFJx4lFyEHREzTTND5pz10fXr9yVH13oxOs0KHREYcdc6jhafkmDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T16:55:56.533267Z"},"content_sha256":"c122e4f049d93322bd5b4c6d78799008775867e1adc6af0b0335675e3184264f","schema_version":"1.0","event_id":"sha256:c122e4f049d93322bd5b4c6d78799008775867e1adc6af0b0335675e3184264f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RT4SHFKY6ZYSFLXMQLBTZ77747/bundle.json","state_url":"https://pith.science/pith/RT4SHFKY6ZYSFLXMQLBTZ77747/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RT4SHFKY6ZYSFLXMQLBTZ77747/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":"2026-08-06T16:55:56Z","links":{"resolver":"https://pith.science/pith/RT4SHFKY6ZYSFLXMQLBTZ77747","bundle":"https://pith.science/pith/RT4SHFKY6ZYSFLXMQLBTZ77747/bundle.json","state":"https://pith.science/pith/RT4SHFKY6ZYSFLXMQLBTZ77747/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RT4SHFKY6ZYSFLXMQLBTZ77747/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:RT4SHFKY6ZYSFLXMQLBTZ77747","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":"7d980dc64112393594469d08efecba0e16c45cd6956bf985d03d7e73daf0f169","cross_cats_sorted":["cs.SY","eess.SY","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-12-31T01:30:14Z","title_canon_sha256":"b78e4cba94de92876da5d48b521b9d4f2cbed59016e399ba1021191abc320e10"},"schema_version":"1.0","source":{"id":"2401.00364","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.00364","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"arxiv_version","alias_value":"2401.00364v2","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.00364","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"pith_short_12","alias_value":"RT4SHFKY6ZYS","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"pith_short_16","alias_value":"RT4SHFKY6ZYSFLXM","created_at":"2026-07-05T11:01:22Z"},{"alias_kind":"pith_short_8","alias_value":"RT4SHFKY","created_at":"2026-07-05T11:01:22Z"}],"graph_snapshots":[{"event_id":"sha256:c122e4f049d93322bd5b4c6d78799008775867e1adc6af0b0335675e3184264f","target":"graph","created_at":"2026-07-05T11:01:22Z","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/2401.00364/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Stochastic approximation (SA) is an iterative algorithm for finding the fixed point of an operator using noisy samples and widely used in optimization and Reinforcement Learning (RL). The noise in RL exhibits a Markovian structure, and in some cases, such as gradient temporal difference (GTD) methods, SA is employed in a two-time-scale framework. This combination introduces significant theoretical challenges for analysis.\n  We derive an upper bound on the error for the iterations of linear two-time-scale SA with Markovian noise. We demonstrate that the mean squared error decreases as $trace (\\","authors_text":"Sajad Khodadadian, Shaan Ul Haque, Siva Theja Maguluri","cross_cats":["cs.SY","eess.SY","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-12-31T01:30:14Z","title":"Tight Finite Time Bounds of Two-Time-Scale Linear Stochastic Approximation with Markovian Noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.00364","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:b1db6ee2feb2ccef7bf4b807c9eb21eb64bdaf3ad7ba9f1777610889bd20801c","target":"record","created_at":"2026-07-05T11:01:22Z","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":"7d980dc64112393594469d08efecba0e16c45cd6956bf985d03d7e73daf0f169","cross_cats_sorted":["cs.SY","eess.SY","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-12-31T01:30:14Z","title_canon_sha256":"b78e4cba94de92876da5d48b521b9d4f2cbed59016e399ba1021191abc320e10"},"schema_version":"1.0","source":{"id":"2401.00364","kind":"arxiv","version":2}},"canonical_sha256":"8cf9239558f67122aeec82c33cffffe7e00d678288d7ce3e71df1a107f5b5418","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cf9239558f67122aeec82c33cffffe7e00d678288d7ce3e71df1a107f5b5418","first_computed_at":"2026-07-05T11:01:22.837360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:01:22.837360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AJyhBUwSFMg+LJGpB4PTD8YnS0beyclth/Rj7Y681LhZolxOMUemb1xp9ou9yqP866FPVsrytEIoKK+RQIIVAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:01:22.837892Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.00364","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1db6ee2feb2ccef7bf4b807c9eb21eb64bdaf3ad7ba9f1777610889bd20801c","sha256:c122e4f049d93322bd5b4c6d78799008775867e1adc6af0b0335675e3184264f"],"state_sha256":"56128e8544e2586fd7da6d319507ca2ef20236e05737ed96c074a493bc736324"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5i3Zll/0PNLn0+A6M4zQdEABnlF+qxEdZLsU4e4A7k5lDWra3xQp85Z5sP9nvRwqT58bqAMV4AwA6MVYvab+Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T16:55:56.541510Z","bundle_sha256":"2983b5405c68710eae9962472b7db7bf88875b0083d25fce87d856d5cf74536e"}}