{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:KZY7DXTWLZGDT3ZL2WPX5XLLNZ","short_pith_number":"pith:KZY7DXTW","canonical_record":{"source":{"id":"1702.02030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-02-07T14:14:19Z","cross_cats_sorted":[],"title_canon_sha256":"1959987fa2d0e7c5ef825d9d8ed4c5afafa4077b882eb5c49d774a4191101749","abstract_canon_sha256":"96ce53fa9790bc9454f06e4f47b667eefaef0a1ddf81123f100da4a4059778a7"},"schema_version":"1.0"},"canonical_sha256":"5671f1de765e4c39ef2bd59f7edd6b6e5cb000e70d2d53aef02a788428a37f35","source":{"kind":"arxiv","id":"1702.02030","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02030","created_at":"2026-05-18T00:51:10Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02030v1","created_at":"2026-05-18T00:51:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02030","created_at":"2026-05-18T00:51:10Z"},{"alias_kind":"pith_short_12","alias_value":"KZY7DXTWLZGD","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"KZY7DXTWLZGDT3ZL","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"KZY7DXTW","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:KZY7DXTWLZGDT3ZL2WPX5XLLNZ","target":"record","payload":{"canonical_record":{"source":{"id":"1702.02030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-02-07T14:14:19Z","cross_cats_sorted":[],"title_canon_sha256":"1959987fa2d0e7c5ef825d9d8ed4c5afafa4077b882eb5c49d774a4191101749","abstract_canon_sha256":"96ce53fa9790bc9454f06e4f47b667eefaef0a1ddf81123f100da4a4059778a7"},"schema_version":"1.0"},"canonical_sha256":"5671f1de765e4c39ef2bd59f7edd6b6e5cb000e70d2d53aef02a788428a37f35","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:10.554367Z","signature_b64":"DhXoEZZJycifK2103Wqm45mNWzfC2QOhCRJ1N/vu253Srm3rzxGyx6mySSl/9B8ZTfCUB7D4Ghcb1itzoFQgDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5671f1de765e4c39ef2bd59f7edd6b6e5cb000e70d2d53aef02a788428a37f35","last_reissued_at":"2026-05-18T00:51:10.553718Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:10.553718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.02030","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":"2026-05-18T00:51:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lZnSgTY2CQKlsxtvfnwtjVBcTxxxm+W9t+5jLxaCS019e9c9s+29EeSw63QIl1uYXw8p8fSE4GILPxiG9nRBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:00:36.749966Z"},"content_sha256":"3b7bcc7b0a3276b3ed1150e3800a852bad3954c74cafa4c784a7957f152d8c0f","schema_version":"1.0","event_id":"sha256:3b7bcc7b0a3276b3ed1150e3800a852bad3954c74cafa4c784a7957f152d8c0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:KZY7DXTWLZGDT3ZL2WPX5XLLNZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Empirical Risk Minimization for Stochastic Convex Optimization: $O(1/n)$- and $O(1/n^2)$-type of Risk Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Lijun Zhang, Rong Jin, Tianbao Yang","submitted_at":"2017-02-07T14:14:19Z","abstract_excerpt":"Although there exist plentiful theories of empirical risk minimization (ERM) for supervised learning, current theoretical understandings of ERM for a related problem---stochastic convex optimization (SCO), are limited. In this work, we strengthen the realm of ERM for SCO by exploiting smoothness and strong convexity conditions to improve the risk bounds. First, we establish an $\\widetilde{O}(d/n + \\sqrt{F_*/n})$ risk bound when the random function is nonnegative, convex and smooth, and the expected function is Lipschitz continuous, where $d$ is the dimensionality of the problem, $n$ is the num"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02030","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":"2026-05-18T00:51:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EyUOoMuQYQ1jERcgLfIueO/kECWTnRSz2ThiiwKmv51SyI/mDHsOO3pljwfghYtzLERvmaRMqTKGVZGwrjw3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:00:36.750617Z"},"content_sha256":"201a76c5776637c64f875fcf0e00ca3fd299e0a0e113cdb50948fe5d4f1e4180","schema_version":"1.0","event_id":"sha256:201a76c5776637c64f875fcf0e00ca3fd299e0a0e113cdb50948fe5d4f1e4180"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KZY7DXTWLZGDT3ZL2WPX5XLLNZ/bundle.json","state_url":"https://pith.science/pith/KZY7DXTWLZGDT3ZL2WPX5XLLNZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KZY7DXTWLZGDT3ZL2WPX5XLLNZ/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":"2026-05-29T17:00:36Z","links":{"resolver":"https://pith.science/pith/KZY7DXTWLZGDT3ZL2WPX5XLLNZ","bundle":"https://pith.science/pith/KZY7DXTWLZGDT3ZL2WPX5XLLNZ/bundle.json","state":"https://pith.science/pith/KZY7DXTWLZGDT3ZL2WPX5XLLNZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KZY7DXTWLZGDT3ZL2WPX5XLLNZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KZY7DXTWLZGDT3ZL2WPX5XLLNZ","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":"96ce53fa9790bc9454f06e4f47b667eefaef0a1ddf81123f100da4a4059778a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-02-07T14:14:19Z","title_canon_sha256":"1959987fa2d0e7c5ef825d9d8ed4c5afafa4077b882eb5c49d774a4191101749"},"schema_version":"1.0","source":{"id":"1702.02030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02030","created_at":"2026-05-18T00:51:10Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02030v1","created_at":"2026-05-18T00:51:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02030","created_at":"2026-05-18T00:51:10Z"},{"alias_kind":"pith_short_12","alias_value":"KZY7DXTWLZGD","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"KZY7DXTWLZGDT3ZL","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"KZY7DXTW","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:201a76c5776637c64f875fcf0e00ca3fd299e0a0e113cdb50948fe5d4f1e4180","target":"graph","created_at":"2026-05-18T00:51:10Z","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":"Although there exist plentiful theories of empirical risk minimization (ERM) for supervised learning, current theoretical understandings of ERM for a related problem---stochastic convex optimization (SCO), are limited. In this work, we strengthen the realm of ERM for SCO by exploiting smoothness and strong convexity conditions to improve the risk bounds. First, we establish an $\\widetilde{O}(d/n + \\sqrt{F_*/n})$ risk bound when the random function is nonnegative, convex and smooth, and the expected function is Lipschitz continuous, where $d$ is the dimensionality of the problem, $n$ is the num","authors_text":"Lijun Zhang, Rong Jin, Tianbao Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-02-07T14:14:19Z","title":"Empirical Risk Minimization for Stochastic Convex Optimization: $O(1/n)$- and $O(1/n^2)$-type of Risk Bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02030","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":"sha256:3b7bcc7b0a3276b3ed1150e3800a852bad3954c74cafa4c784a7957f152d8c0f","target":"record","created_at":"2026-05-18T00:51:10Z","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":"96ce53fa9790bc9454f06e4f47b667eefaef0a1ddf81123f100da4a4059778a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-02-07T14:14:19Z","title_canon_sha256":"1959987fa2d0e7c5ef825d9d8ed4c5afafa4077b882eb5c49d774a4191101749"},"schema_version":"1.0","source":{"id":"1702.02030","kind":"arxiv","version":1}},"canonical_sha256":"5671f1de765e4c39ef2bd59f7edd6b6e5cb000e70d2d53aef02a788428a37f35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5671f1de765e4c39ef2bd59f7edd6b6e5cb000e70d2d53aef02a788428a37f35","first_computed_at":"2026-05-18T00:51:10.553718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:10.553718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DhXoEZZJycifK2103Wqm45mNWzfC2QOhCRJ1N/vu253Srm3rzxGyx6mySSl/9B8ZTfCUB7D4Ghcb1itzoFQgDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:10.554367Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.02030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b7bcc7b0a3276b3ed1150e3800a852bad3954c74cafa4c784a7957f152d8c0f","sha256:201a76c5776637c64f875fcf0e00ca3fd299e0a0e113cdb50948fe5d4f1e4180"],"state_sha256":"c0d1e98e0c348fe7ba587dd4d47ac0af689db82274cd70a952daeb89cfeac257"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z3EO7efVPw5Nc387G6EUjNFU0MEIx3P3yX7f74QoqBHeUVBoKQKG3xUlbP3LX1rUQ4WXPTlfn5P55f7+XOmKCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:00:36.752939Z","bundle_sha256":"808626938811b527a3fd99805154defb55b5848784bcc735705f2fd9f4508fd5"}}