{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:REHYKA5SIRBEWP42FHEL4QAYDO","short_pith_number":"pith:REHYKA5S","canonical_record":{"source":{"id":"1803.07374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-20T11:27:01Z","cross_cats_sorted":["cs.CC","cs.NA","math.NA"],"title_canon_sha256":"31002c689665cbcdec0f722970894027b76ff50466ee19a445a7ed10e46a74e9","abstract_canon_sha256":"02624a5200ac3a28963c66ea5a07faba3200f821f47d348952ac606d73cf5877"},"schema_version":"1.0"},"canonical_sha256":"890f8503b244424b3f9a29c8be40181bb0293d6d4b6359e3b59367b987ff719a","source":{"kind":"arxiv","id":"1803.07374","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07374","created_at":"2026-05-18T00:20:22Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07374v1","created_at":"2026-05-18T00:20:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07374","created_at":"2026-05-18T00:20:22Z"},{"alias_kind":"pith_short_12","alias_value":"REHYKA5SIRBE","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"REHYKA5SIRBEWP42","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"REHYKA5S","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:REHYKA5SIRBEWP42FHEL4QAYDO","target":"record","payload":{"canonical_record":{"source":{"id":"1803.07374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-20T11:27:01Z","cross_cats_sorted":["cs.CC","cs.NA","math.NA"],"title_canon_sha256":"31002c689665cbcdec0f722970894027b76ff50466ee19a445a7ed10e46a74e9","abstract_canon_sha256":"02624a5200ac3a28963c66ea5a07faba3200f821f47d348952ac606d73cf5877"},"schema_version":"1.0"},"canonical_sha256":"890f8503b244424b3f9a29c8be40181bb0293d6d4b6359e3b59367b987ff719a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:22.688368Z","signature_b64":"3hQgbxPlsql8QztwaDhLNtuuk2BOn7DMeOfhGpcuuNSJHk66KWmbbB/0MvLRLl7hjlr7/dJTyxDCwbcDpnnNDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"890f8503b244424b3f9a29c8be40181bb0293d6d4b6359e3b59367b987ff719a","last_reissued_at":"2026-05-18T00:20:22.687759Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:22.687759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.07374","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qA0AGmVgxB0pVQGcXrtVIFulxv3ms2UyyprwI2Comr7XV/d0WOmX4lzzvNP2K1Jnls5KBfZChCLG5LURH04ECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T02:08:07.750940Z"},"content_sha256":"315629908c05af58ecf5c8a0fc6d1247b42bdb7b9a703f2270b014aa7400ae19","schema_version":"1.0","event_id":"sha256:315629908c05af58ecf5c8a0fc6d1247b42bdb7b9a703f2270b014aa7400ae19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:REHYKA5SIRBEWP42FHEL4QAYDO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fastest Rates for Stochastic Mirror Descent Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.NA","math.NA"],"primary_cat":"math.OC","authors_text":"Filip Hanzely, Peter Richt\\'arik","submitted_at":"2018-03-20T11:27:01Z","abstract_excerpt":"Relative smoothness - a notion introduced by Birnbaum et al. (2011) and rediscovered by Bauschke et al. (2016) and Lu et al. (2016) - generalizes the standard notion of smoothness typically used in the analysis of gradient type methods. In this work we are taking ideas from well studied field of stochastic convex optimization and using them in order to obtain faster algorithms for minimizing relatively smooth functions. We propose and analyze two new algorithms: Relative Randomized Coordinate Descent (relRCD) and Relative Stochastic Gradient Descent (relSGD), both generalizing famous algorithm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07374","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:20:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L062k9hh3OM7gUTQuOyoVeRksknrP91I7harWKsavdDxP+CCEn36mdcjpn9R9OQaiBo3GM9pY2rft4pustyHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T02:08:07.751724Z"},"content_sha256":"45f3f0db85518be1fe3b7c26d332de5725fd904338f70cd23dc494bdef116071","schema_version":"1.0","event_id":"sha256:45f3f0db85518be1fe3b7c26d332de5725fd904338f70cd23dc494bdef116071"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/REHYKA5SIRBEWP42FHEL4QAYDO/bundle.json","state_url":"https://pith.science/pith/REHYKA5SIRBEWP42FHEL4QAYDO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/REHYKA5SIRBEWP42FHEL4QAYDO/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":"2026-05-24T02:08:07Z","links":{"resolver":"https://pith.science/pith/REHYKA5SIRBEWP42FHEL4QAYDO","bundle":"https://pith.science/pith/REHYKA5SIRBEWP42FHEL4QAYDO/bundle.json","state":"https://pith.science/pith/REHYKA5SIRBEWP42FHEL4QAYDO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/REHYKA5SIRBEWP42FHEL4QAYDO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:REHYKA5SIRBEWP42FHEL4QAYDO","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":"02624a5200ac3a28963c66ea5a07faba3200f821f47d348952ac606d73cf5877","cross_cats_sorted":["cs.CC","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-20T11:27:01Z","title_canon_sha256":"31002c689665cbcdec0f722970894027b76ff50466ee19a445a7ed10e46a74e9"},"schema_version":"1.0","source":{"id":"1803.07374","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07374","created_at":"2026-05-18T00:20:22Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07374v1","created_at":"2026-05-18T00:20:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07374","created_at":"2026-05-18T00:20:22Z"},{"alias_kind":"pith_short_12","alias_value":"REHYKA5SIRBE","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"REHYKA5SIRBEWP42","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"REHYKA5S","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:45f3f0db85518be1fe3b7c26d332de5725fd904338f70cd23dc494bdef116071","target":"graph","created_at":"2026-05-18T00:20:22Z","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"},"paper":{"abstract_excerpt":"Relative smoothness - a notion introduced by Birnbaum et al. (2011) and rediscovered by Bauschke et al. (2016) and Lu et al. (2016) - generalizes the standard notion of smoothness typically used in the analysis of gradient type methods. In this work we are taking ideas from well studied field of stochastic convex optimization and using them in order to obtain faster algorithms for minimizing relatively smooth functions. We propose and analyze two new algorithms: Relative Randomized Coordinate Descent (relRCD) and Relative Stochastic Gradient Descent (relSGD), both generalizing famous algorithm","authors_text":"Filip Hanzely, Peter Richt\\'arik","cross_cats":["cs.CC","cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-20T11:27:01Z","title":"Fastest Rates for Stochastic Mirror Descent Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07374","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":"sha256:315629908c05af58ecf5c8a0fc6d1247b42bdb7b9a703f2270b014aa7400ae19","target":"record","created_at":"2026-05-18T00:20:22Z","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":"02624a5200ac3a28963c66ea5a07faba3200f821f47d348952ac606d73cf5877","cross_cats_sorted":["cs.CC","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-20T11:27:01Z","title_canon_sha256":"31002c689665cbcdec0f722970894027b76ff50466ee19a445a7ed10e46a74e9"},"schema_version":"1.0","source":{"id":"1803.07374","kind":"arxiv","version":1}},"canonical_sha256":"890f8503b244424b3f9a29c8be40181bb0293d6d4b6359e3b59367b987ff719a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"890f8503b244424b3f9a29c8be40181bb0293d6d4b6359e3b59367b987ff719a","first_computed_at":"2026-05-18T00:20:22.687759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:22.687759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3hQgbxPlsql8QztwaDhLNtuuk2BOn7DMeOfhGpcuuNSJHk66KWmbbB/0MvLRLl7hjlr7/dJTyxDCwbcDpnnNDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:22.688368Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.07374","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:315629908c05af58ecf5c8a0fc6d1247b42bdb7b9a703f2270b014aa7400ae19","sha256:45f3f0db85518be1fe3b7c26d332de5725fd904338f70cd23dc494bdef116071"],"state_sha256":"470f470ccf4a9b1190e761b9b6fd24732a60b8a630a1095fe3869982762053a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hAeMckFtXGanxoDN4bFN/P7h8SqTSrin0coAAfV/hfD0lE721tT4oxCjbtvys+aHc9CfmD6XRYdev0kmqwOyDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T02:08:07.755514Z","bundle_sha256":"ab201e1d1ef2e38c9813fe94317d7fe4114659b9aef20f32ae4cbea80d4e1f6d"}}