{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:SL2F4IL2IDKRU5JIIX3C2ZFQ4U","short_pith_number":"pith:SL2F4IL2","schema_version":"1.0","canonical_sha256":"92f45e217a40d51a752845f62d64b0e5160c830446828bb20961db628419e2d3","source":{"kind":"arxiv","id":"1510.01444","version":5},"attestation_state":"computed","paper":{"title":"Stochastic subGradient Methods with Linear Convergence for Polyhedral Convex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Qihang Lin, Tianbao Yang","submitted_at":"2015-10-06T06:17:56Z","abstract_excerpt":"In this paper, we show that simple {Stochastic} subGradient Decent methods with multiple Restarting, named {\\bf RSGD}, can achieve a \\textit{linear convergence rate} for a class of non-smooth and non-strongly convex optimization problems where the epigraph of the objective function is a polyhedron, to which we refer as {\\bf polyhedral convex optimization}. Its applications in machine learning include $\\ell_1$ constrained or regularized piecewise linear loss minimization and submodular function minimization. To the best of our knowledge, this is the first result on the linear convergence rate o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.01444","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-10-06T06:17:56Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"66d810e7ddb66ed8b82e920047911569b96438f8240f3a3761e1d8c615dce85c","abstract_canon_sha256":"99d9f1c5b4008a7c977d0cfa961fb6f09733301a40e53b4c520020a4fb7cebbf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:59.675547Z","signature_b64":"9Cd+kKuzzL16kZ6MP0uTLtBYUOAP2qP7KjFgHfsKPT2Sveu0+QvNeU5M4C7JOZ9Z3YC7yP5GoOJgj1kVvutvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92f45e217a40d51a752845f62d64b0e5160c830446828bb20961db628419e2d3","last_reissued_at":"2026-05-18T01:17:59.674849Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:59.674849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic subGradient Methods with Linear Convergence for Polyhedral Convex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Qihang Lin, Tianbao Yang","submitted_at":"2015-10-06T06:17:56Z","abstract_excerpt":"In this paper, we show that simple {Stochastic} subGradient Decent methods with multiple Restarting, named {\\bf RSGD}, can achieve a \\textit{linear convergence rate} for a class of non-smooth and non-strongly convex optimization problems where the epigraph of the objective function is a polyhedron, to which we refer as {\\bf polyhedral convex optimization}. Its applications in machine learning include $\\ell_1$ constrained or regularized piecewise linear loss minimization and submodular function minimization. To the best of our knowledge, this is the first result on the linear convergence rate o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01444","kind":"arxiv","version":5},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.01444","created_at":"2026-05-18T01:17:59.674972+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.01444v5","created_at":"2026-05-18T01:17:59.674972+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01444","created_at":"2026-05-18T01:17:59.674972+00:00"},{"alias_kind":"pith_short_12","alias_value":"SL2F4IL2IDKR","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"SL2F4IL2IDKRU5JI","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"SL2F4IL2","created_at":"2026-05-18T12:29:42.218222+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"1608.03983","citing_title":"SGDR: Stochastic Gradient Descent with Warm Restarts","ref_index":16,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SL2F4IL2IDKRU5JIIX3C2ZFQ4U","json":"https://pith.science/pith/SL2F4IL2IDKRU5JIIX3C2ZFQ4U.json","graph_json":"https://pith.science/api/pith-number/SL2F4IL2IDKRU5JIIX3C2ZFQ4U/graph.json","events_json":"https://pith.science/api/pith-number/SL2F4IL2IDKRU5JIIX3C2ZFQ4U/events.json","paper":"https://pith.science/paper/SL2F4IL2"},"agent_actions":{"view_html":"https://pith.science/pith/SL2F4IL2IDKRU5JIIX3C2ZFQ4U","download_json":"https://pith.science/pith/SL2F4IL2IDKRU5JIIX3C2ZFQ4U.json","view_paper":"https://pith.science/paper/SL2F4IL2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.01444&json=true","fetch_graph":"https://pith.science/api/pith-number/SL2F4IL2IDKRU5JIIX3C2ZFQ4U/graph.json","fetch_events":"https://pith.science/api/pith-number/SL2F4IL2IDKRU5JIIX3C2ZFQ4U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SL2F4IL2IDKRU5JIIX3C2ZFQ4U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SL2F4IL2IDKRU5JIIX3C2ZFQ4U/action/storage_attestation","attest_author":"https://pith.science/pith/SL2F4IL2IDKRU5JIIX3C2ZFQ4U/action/author_attestation","sign_citation":"https://pith.science/pith/SL2F4IL2IDKRU5JIIX3C2ZFQ4U/action/citation_signature","submit_replication":"https://pith.science/pith/SL2F4IL2IDKRU5JIIX3C2ZFQ4U/action/replication_record"}},"created_at":"2026-05-18T01:17:59.674972+00:00","updated_at":"2026-05-18T01:17:59.674972+00:00"}