{"paper":{"title":"Incremental Gradient Descent with Small Epoch Counts is Surprisingly Slow on Ill-Conditioned Problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Chulhee Yun, Jaeyoung Cha, Yujun Kim","submitted_at":"2025-06-04T16:17:25Z","abstract_excerpt":"Recent theoretical results demonstrate that the convergence rates of permutation-based SGD (e.g., random reshuffling SGD) are faster than uniform-sampling SGD; however, these studies focus mainly on the large epoch regime, where the number of epochs $K$ exceeds the condition number $\\kappa$. In contrast, little is known when $K$ is smaller than $\\kappa$, and it is still a challenging open question whether permutation-based SGD can converge faster in this small epoch regime (Safran and Shamir, 2021). As a step toward understanding this gap, we study the naive deterministic variant, Incremental "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04126","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.04126/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"}