{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OJKWBCG6SAUPZ7KU45XSEGRLYZ","short_pith_number":"pith:OJKWBCG6","canonical_record":{"source":{"id":"1306.3721","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-06-17T01:27:10Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"c9d428ddc2261cda69a8ff4e9b0e80cbacb99a79d8faa16131a60a0efa389ef8","abstract_canon_sha256":"71207173dc8493a62bebe7eb8c27bb4c2d46bd2c140236068d94cef9c42cde69"},"schema_version":"1.0"},"canonical_sha256":"72556088de9028fcfd54e76f221a2bc649707b76d04ca5a488b9dda0ad553ff0","source":{"kind":"arxiv","id":"1306.3721","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3721","created_at":"2026-05-18T03:18:51Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3721v2","created_at":"2026-05-18T03:18:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3721","created_at":"2026-05-18T03:18:51Z"},{"alias_kind":"pith_short_12","alias_value":"OJKWBCG6SAUP","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OJKWBCG6SAUPZ7KU","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OJKWBCG6","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OJKWBCG6SAUPZ7KU45XSEGRLYZ","target":"record","payload":{"canonical_record":{"source":{"id":"1306.3721","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-06-17T01:27:10Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"c9d428ddc2261cda69a8ff4e9b0e80cbacb99a79d8faa16131a60a0efa389ef8","abstract_canon_sha256":"71207173dc8493a62bebe7eb8c27bb4c2d46bd2c140236068d94cef9c42cde69"},"schema_version":"1.0"},"canonical_sha256":"72556088de9028fcfd54e76f221a2bc649707b76d04ca5a488b9dda0ad553ff0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:51.115964Z","signature_b64":"qdbLg1mEfxxLpcFmaDKPsyWKUziJjchymokdOlQCLAC0gnrOYsLS6fG+YjeWryQn3nrl4JrnniVvXu2AETbLAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72556088de9028fcfd54e76f221a2bc649707b76d04ca5a488b9dda0ad553ff0","last_reissued_at":"2026-05-18T03:18:51.115456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:51.115456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.3721","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":"2026-05-18T03:18:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AQPv5h5UIQCFIjKwle7dL2EkTdnES4neSoaeSD5z7tzfHBt5Y5gof828q8E6DylsNYUnB/PgROhh/GQijfVdBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T09:54:44.318185Z"},"content_sha256":"34727b01a1923c9602f7f474c990dc3845df102111f0d7f62ba96921b49bb3fd","schema_version":"1.0","event_id":"sha256:34727b01a1923c9602f7f474c990dc3845df102111f0d7f62ba96921b49bb3fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OJKWBCG6SAUPZ7KU45XSEGRLYZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Online Alternating Direction Method (longer version)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Arindam Banerjee, Huahua Wang","submitted_at":"2013-06-17T01:27:10Z","abstract_excerpt":"Online optimization has emerged as powerful tool in large scale optimization. In this pa- per, we introduce efficient online optimization algorithms based on the alternating direction method (ADM), which can solve online convex optimization under linear constraints where the objective could be non-smooth. We introduce new proof techniques for ADM in the batch setting, which yields a O(1/T) convergence rate for ADM and forms the basis for regret anal- ysis in the online setting. We consider two scenarios in the online setting, based on whether an additional Bregman divergence is needed or not. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3721","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":""},"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":"2026-05-18T03:18:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LDXOtValZlcxWBe1J+KXTtmuxh3oLtNH5wJPqKQQwPA5C+vfwyPhzZX1Wnn6wMmqTLXF7KRwrCftDFIWGB1HDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T09:54:44.318546Z"},"content_sha256":"ad07be5f8580c9c2800a8f8704ea05c6e503698940eaf41e684c1ad3b7f3ad1a","schema_version":"1.0","event_id":"sha256:ad07be5f8580c9c2800a8f8704ea05c6e503698940eaf41e684c1ad3b7f3ad1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OJKWBCG6SAUPZ7KU45XSEGRLYZ/bundle.json","state_url":"https://pith.science/pith/OJKWBCG6SAUPZ7KU45XSEGRLYZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OJKWBCG6SAUPZ7KU45XSEGRLYZ/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":"2026-06-20T09:54:44Z","links":{"resolver":"https://pith.science/pith/OJKWBCG6SAUPZ7KU45XSEGRLYZ","bundle":"https://pith.science/pith/OJKWBCG6SAUPZ7KU45XSEGRLYZ/bundle.json","state":"https://pith.science/pith/OJKWBCG6SAUPZ7KU45XSEGRLYZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OJKWBCG6SAUPZ7KU45XSEGRLYZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OJKWBCG6SAUPZ7KU45XSEGRLYZ","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":"71207173dc8493a62bebe7eb8c27bb4c2d46bd2c140236068d94cef9c42cde69","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-06-17T01:27:10Z","title_canon_sha256":"c9d428ddc2261cda69a8ff4e9b0e80cbacb99a79d8faa16131a60a0efa389ef8"},"schema_version":"1.0","source":{"id":"1306.3721","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3721","created_at":"2026-05-18T03:18:51Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3721v2","created_at":"2026-05-18T03:18:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3721","created_at":"2026-05-18T03:18:51Z"},{"alias_kind":"pith_short_12","alias_value":"OJKWBCG6SAUP","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OJKWBCG6SAUPZ7KU","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OJKWBCG6","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:ad07be5f8580c9c2800a8f8704ea05c6e503698940eaf41e684c1ad3b7f3ad1a","target":"graph","created_at":"2026-05-18T03:18:51Z","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":"Online optimization has emerged as powerful tool in large scale optimization. In this pa- per, we introduce efficient online optimization algorithms based on the alternating direction method (ADM), which can solve online convex optimization under linear constraints where the objective could be non-smooth. We introduce new proof techniques for ADM in the batch setting, which yields a O(1/T) convergence rate for ADM and forms the basis for regret anal- ysis in the online setting. We consider two scenarios in the online setting, based on whether an additional Bregman divergence is needed or not. ","authors_text":"Arindam Banerjee, Huahua Wang","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-06-17T01:27:10Z","title":"Online Alternating Direction Method (longer version)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3721","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":"sha256:34727b01a1923c9602f7f474c990dc3845df102111f0d7f62ba96921b49bb3fd","target":"record","created_at":"2026-05-18T03:18:51Z","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":"71207173dc8493a62bebe7eb8c27bb4c2d46bd2c140236068d94cef9c42cde69","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-06-17T01:27:10Z","title_canon_sha256":"c9d428ddc2261cda69a8ff4e9b0e80cbacb99a79d8faa16131a60a0efa389ef8"},"schema_version":"1.0","source":{"id":"1306.3721","kind":"arxiv","version":2}},"canonical_sha256":"72556088de9028fcfd54e76f221a2bc649707b76d04ca5a488b9dda0ad553ff0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72556088de9028fcfd54e76f221a2bc649707b76d04ca5a488b9dda0ad553ff0","first_computed_at":"2026-05-18T03:18:51.115456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:51.115456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qdbLg1mEfxxLpcFmaDKPsyWKUziJjchymokdOlQCLAC0gnrOYsLS6fG+YjeWryQn3nrl4JrnniVvXu2AETbLAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:51.115964Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.3721","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34727b01a1923c9602f7f474c990dc3845df102111f0d7f62ba96921b49bb3fd","sha256:ad07be5f8580c9c2800a8f8704ea05c6e503698940eaf41e684c1ad3b7f3ad1a"],"state_sha256":"7af335f2d46dcbb7714da64d9dc44f46d6728eab8ffead0ff90930ef4665bc02"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HBgVXGDB4ALxVCnsqvxvbSrkHcKQjbu0J/HzQ3pzatrg2Va1/s72UVN9ndRYJoTU85zKiQaJ2rMxmxfP0m7FBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T09:54:44.320482Z","bundle_sha256":"eef618c5cebce98d4873607e7abea304d1bf3c3a64637554823ebb92746ba7f3"}}