{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5MCHTVTLKHRESRP4R5JRRNYJU3","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":"c90530341b013137bccb3779e44f444c2d7f5c0eb973e000214d342862d385e4","cross_cats_sorted":["cs.LG","cs.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2024-10-16T21:49:27Z","title_canon_sha256":"2b7258bd863b9a5d915960aeb8e8e5fd9a80119d11ccc8f714cd12e00262993f"},"schema_version":"1.0","source":{"id":"2410.13067","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.13067","created_at":"2026-07-05T10:18:43Z"},{"alias_kind":"arxiv_version","alias_value":"2410.13067v1","created_at":"2026-07-05T10:18:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.13067","created_at":"2026-07-05T10:18:43Z"},{"alias_kind":"pith_short_12","alias_value":"5MCHTVTLKHRE","created_at":"2026-07-05T10:18:43Z"},{"alias_kind":"pith_short_16","alias_value":"5MCHTVTLKHRESRP4","created_at":"2026-07-05T10:18:43Z"},{"alias_kind":"pith_short_8","alias_value":"5MCHTVTL","created_at":"2026-07-05T10:18:43Z"}],"graph_snapshots":[{"event_id":"sha256:3e64b7f1b420318f3f7fe0280d6d9f13a2ce0bda49e5841b73e5814ba1d44dad","target":"graph","created_at":"2026-07-05T10:18:43Z","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/2410.13067/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Previous studies on two-timescale stochastic approximation (SA) mainly focused on bounding mean-squared errors under diminishing stepsize schemes. In this work, we investigate {\\it constant} stpesize schemes through the lens of Markov processes, proving that the iterates of both timescales converge to a unique joint stationary distribution in Wasserstein metric. We derive explicit geometric and non-asymptotic convergence rates, as well as the variance and bias introduced by constant stepsizes in the presence of Markovian noise. Specifically, with two constant stepsizes $\\alpha < \\beta$, we sho","authors_text":"Jeongyeol Kwon, Luke Dotson, Qiaomin Xie, Yudong Chen","cross_cats":["cs.LG","cs.SY","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2024-10-16T21:49:27Z","title":"Two-Timescale Linear Stochastic Approximation: Constant Stepsizes Go a Long Way"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.13067","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":"sha256:8a906e09e23d0a81231558fc66e172f6d794da487a6c6a24edf8cffad05bd8f9","target":"record","created_at":"2026-07-05T10:18:43Z","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":"c90530341b013137bccb3779e44f444c2d7f5c0eb973e000214d342862d385e4","cross_cats_sorted":["cs.LG","cs.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2024-10-16T21:49:27Z","title_canon_sha256":"2b7258bd863b9a5d915960aeb8e8e5fd9a80119d11ccc8f714cd12e00262993f"},"schema_version":"1.0","source":{"id":"2410.13067","kind":"arxiv","version":1}},"canonical_sha256":"eb0479d66b51e24945fc8f5318b709a6c93e42788b1e5692a2b8af410715f641","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb0479d66b51e24945fc8f5318b709a6c93e42788b1e5692a2b8af410715f641","first_computed_at":"2026-07-05T10:18:43.519213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:18:43.519213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZLhPnpShVWNRchwQzEA/tMr1ya61ab4OOjjlSoRotNDyhCV1gI4JcaHmngc+jelGS9pgOKBuVRqV8H/CpI8XBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:18:43.519728Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.13067","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a906e09e23d0a81231558fc66e172f6d794da487a6c6a24edf8cffad05bd8f9","sha256:3e64b7f1b420318f3f7fe0280d6d9f13a2ce0bda49e5841b73e5814ba1d44dad"],"state_sha256":"e11b47df7b7c7b575dc62acfb3a85a7e5926ba5299b3820e068f2cf17dbbab10"}