{"paper":{"title":"High Probability Convergence of Clipped-SGD Under Heavy-tailed Noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alina Ene, Huy Le Nguyen, Ta Duy Nguyen, Thien Hang Nguyen","submitted_at":"2023-02-10T18:54:51Z","abstract_excerpt":"While the convergence behaviors of stochastic gradient methods are well understood \\emph{in expectation}, there still exist many gaps in the understanding of their convergence with \\emph{high probability}, where the convergence rate has a logarithmic dependency on the desired success probability parameter. In the \\emph{heavy-tailed noise} setting, where the stochastic gradient noise only has bounded $p$-th moments for some $p\\in(1,2]$, existing works could only show bounds \\emph{in expectation} for a variant of stochastic gradient descent (SGD) with clipped gradients, or high probability bound"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.05437","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.05437/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}