{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:F7G6J4OCW2HYD5IOLWHKBMJVBC","short_pith_number":"pith:F7G6J4OC","canonical_record":{"source":{"id":"1909.04299","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-09-10T05:27:58Z","cross_cats_sorted":["cs.LG","cs.SY","eess.SY","math.OC"],"title_canon_sha256":"6d98aade30d29cd3232f4145f820c88efe8bcbbf49d86bdd873f959a3b111582","abstract_canon_sha256":"f9734dc7d961b81d111c18425d6ff4c2cc79b9e1565452180898b88cbfa64be2"},"schema_version":"1.0"},"canonical_sha256":"2fcde4f1c2b68f81f50e5d8ea0b135088b28ca1dcf05fc4511f4e4db9e77b3cb","source":{"kind":"arxiv","id":"1909.04299","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.04299","created_at":"2026-07-05T01:31:49Z"},{"alias_kind":"arxiv_version","alias_value":"1909.04299v3","created_at":"2026-07-05T01:31:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.04299","created_at":"2026-07-05T01:31:49Z"},{"alias_kind":"pith_short_12","alias_value":"F7G6J4OCW2HY","created_at":"2026-07-05T01:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"F7G6J4OCW2HYD5IO","created_at":"2026-07-05T01:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"F7G6J4OC","created_at":"2026-07-05T01:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:F7G6J4OCW2HYD5IOLWHKBMJVBC","target":"record","payload":{"canonical_record":{"source":{"id":"1909.04299","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-09-10T05:27:58Z","cross_cats_sorted":["cs.LG","cs.SY","eess.SY","math.OC"],"title_canon_sha256":"6d98aade30d29cd3232f4145f820c88efe8bcbbf49d86bdd873f959a3b111582","abstract_canon_sha256":"f9734dc7d961b81d111c18425d6ff4c2cc79b9e1565452180898b88cbfa64be2"},"schema_version":"1.0"},"canonical_sha256":"2fcde4f1c2b68f81f50e5d8ea0b135088b28ca1dcf05fc4511f4e4db9e77b3cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:31:49.618263Z","signature_b64":"9wrpJYjLWawIAtSTY/mvaQ8Kfb0S8JK3T87nVIAXZrXHERNDUZgrhxEeW5rhqkHVYFt8z3ld1l8ETc3Qj67wBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fcde4f1c2b68f81f50e5d8ea0b135088b28ca1dcf05fc4511f4e4db9e77b3cb","last_reissued_at":"2026-07-05T01:31:49.617794Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:31:49.617794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1909.04299","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:31:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6AfAwMje26+ovuyBBobdjxqLuZiZKlBpRLOp0rUGTdyxeaqcv5ITGxhcquP2H9GUdSVVdgxLty6+L7kcEA3YDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T09:04:40.119698Z"},"content_sha256":"0cd493acde299591355a4cb37d413cef37dbefcf3b89c84888691708d6130391","schema_version":"1.0","event_id":"sha256:0cd493acde299591355a4cb37d413cef37dbefcf3b89c84888691708d6130391"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:F7G6J4OCW2HYD5IOLWHKBMJVBC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Multistep Lyapunov Approach for Finite-Time Analysis of Biased Stochastic Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.SY","eess.SY","math.OC"],"primary_cat":"stat.ML","authors_text":"Bingcong Li, Gang Wang, Georgios B. Giannakis","submitted_at":"2019-09-10T05:27:58Z","abstract_excerpt":"Motivated by the widespread use of temporal-difference (TD-) and Q-learning algorithms in reinforcement learning, this paper studies a class of biased stochastic approximation (SA) procedures under a mild \"ergodic-like\" assumption on the underlying stochastic noise sequence. Building upon a carefully designed multistep Lyapunov function that looks ahead to several future updates to accommodate the stochastic perturbations (for control of the gradient bias), we prove a general result on the convergence of the iterates, and use it to derive non-asymptotic bounds on the mean-square error in the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.04299","kind":"arxiv","version":3},"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/1909.04299/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":"2026-07-05T01:31:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eD6xNO82lkLUavH2o4vC0OwNFZhZ8VjPV5kdSqWyebrFUaD0CM5xQEX8oQhfHkrOGgS/sKMDJnGyzTjqs05jBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T09:04:40.120077Z"},"content_sha256":"8295970e2fc30d26a7c4c4a10370aa0370b1daa252af5f771ca9355d47e94f06","schema_version":"1.0","event_id":"sha256:8295970e2fc30d26a7c4c4a10370aa0370b1daa252af5f771ca9355d47e94f06"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F7G6J4OCW2HYD5IOLWHKBMJVBC/bundle.json","state_url":"https://pith.science/pith/F7G6J4OCW2HYD5IOLWHKBMJVBC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F7G6J4OCW2HYD5IOLWHKBMJVBC/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":"2026-07-05T09:04:40Z","links":{"resolver":"https://pith.science/pith/F7G6J4OCW2HYD5IOLWHKBMJVBC","bundle":"https://pith.science/pith/F7G6J4OCW2HYD5IOLWHKBMJVBC/bundle.json","state":"https://pith.science/pith/F7G6J4OCW2HYD5IOLWHKBMJVBC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F7G6J4OCW2HYD5IOLWHKBMJVBC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:F7G6J4OCW2HYD5IOLWHKBMJVBC","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":"f9734dc7d961b81d111c18425d6ff4c2cc79b9e1565452180898b88cbfa64be2","cross_cats_sorted":["cs.LG","cs.SY","eess.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-09-10T05:27:58Z","title_canon_sha256":"6d98aade30d29cd3232f4145f820c88efe8bcbbf49d86bdd873f959a3b111582"},"schema_version":"1.0","source":{"id":"1909.04299","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.04299","created_at":"2026-07-05T01:31:49Z"},{"alias_kind":"arxiv_version","alias_value":"1909.04299v3","created_at":"2026-07-05T01:31:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.04299","created_at":"2026-07-05T01:31:49Z"},{"alias_kind":"pith_short_12","alias_value":"F7G6J4OCW2HY","created_at":"2026-07-05T01:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"F7G6J4OCW2HYD5IO","created_at":"2026-07-05T01:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"F7G6J4OC","created_at":"2026-07-05T01:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:8295970e2fc30d26a7c4c4a10370aa0370b1daa252af5f771ca9355d47e94f06","target":"graph","created_at":"2026-07-05T01:31:49Z","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/1909.04299/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by the widespread use of temporal-difference (TD-) and Q-learning algorithms in reinforcement learning, this paper studies a class of biased stochastic approximation (SA) procedures under a mild \"ergodic-like\" assumption on the underlying stochastic noise sequence. Building upon a carefully designed multistep Lyapunov function that looks ahead to several future updates to accommodate the stochastic perturbations (for control of the gradient bias), we prove a general result on the convergence of the iterates, and use it to derive non-asymptotic bounds on the mean-square error in the c","authors_text":"Bingcong Li, Gang Wang, Georgios B. Giannakis","cross_cats":["cs.LG","cs.SY","eess.SY","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-09-10T05:27:58Z","title":"A Multistep Lyapunov Approach for Finite-Time Analysis of Biased Stochastic Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.04299","kind":"arxiv","version":3},"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":"sha256:0cd493acde299591355a4cb37d413cef37dbefcf3b89c84888691708d6130391","target":"record","created_at":"2026-07-05T01:31:49Z","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":"f9734dc7d961b81d111c18425d6ff4c2cc79b9e1565452180898b88cbfa64be2","cross_cats_sorted":["cs.LG","cs.SY","eess.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-09-10T05:27:58Z","title_canon_sha256":"6d98aade30d29cd3232f4145f820c88efe8bcbbf49d86bdd873f959a3b111582"},"schema_version":"1.0","source":{"id":"1909.04299","kind":"arxiv","version":3}},"canonical_sha256":"2fcde4f1c2b68f81f50e5d8ea0b135088b28ca1dcf05fc4511f4e4db9e77b3cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fcde4f1c2b68f81f50e5d8ea0b135088b28ca1dcf05fc4511f4e4db9e77b3cb","first_computed_at":"2026-07-05T01:31:49.617794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:31:49.617794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9wrpJYjLWawIAtSTY/mvaQ8Kfb0S8JK3T87nVIAXZrXHERNDUZgrhxEeW5rhqkHVYFt8z3ld1l8ETc3Qj67wBg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:31:49.618263Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.04299","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0cd493acde299591355a4cb37d413cef37dbefcf3b89c84888691708d6130391","sha256:8295970e2fc30d26a7c4c4a10370aa0370b1daa252af5f771ca9355d47e94f06"],"state_sha256":"4be1bb2ada29332595abe6db84dc50d288d62d2bd3e14cf9e84fa571d4cc8798"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QwtXCTgjQURnFsyC0ZqdA0Swm0K/MxXgnA0fXjkvl3q7/p9w+d/wM0UVlxsDUG7UbUjpLebzA2sNNG8IQvfUAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T09:04:40.122214Z","bundle_sha256":"8871bd6162397c3bcce65314d3d1279d7b68875107df83401d3ffd5975a008b3"}}