{"work":{"id":"9bf7e268-b9d5-4702-bb0a-14a1a4cd49b4","openalex_id":"https://openalex.org/W1916951228","doi":"10.48550/arxiv.1308.6370","arxiv_id":"1308.6370","raw_key":null,"title":"Fast Convergence of Stochastic Gradient Descent under a Strong Growth Condition","authors":null,"authors_text":"Fast convergence of stochastic gradient descent under a strong growth condition , author=","year":2013,"venue":"math.OC","abstract":"We consider optimizing a function smooth convex function $f$ that is the average of a set of differentiable functions $f_i$, under the assumption considered by Solodov [1998] and Tseng [1998] that the norm of each gradient $f_i'$ is bounded by a linear function of the norm of the average gradient $f'$. We show that under these assumptions the basic stochastic gradient method with a sufficiently-small constant step-size has an $O(1/k)$ convergence rate, and has a linear convergence rate if $g$ is strongly-convex.","external_url":"https://arxiv.org/abs/1308.6370","cited_by_count":86,"metadata_source":"pith","metadata_fetched_at":"2026-08-05T02:28:24.338817+00:00","pith_arxiv_id":"1308.6370","created_at":"2026-05-11T02:30:52.211876+00:00","updated_at":"2026-08-05T02:28:24.338817+00:00","title_quality_ok":true,"display_title":"Fast Convergence of Stochastic Gradient Descent under a Strong Growth Condition","render_title":"Fast Convergence of Stochastic Gradient Descent under a Strong Growth Condition"},"hub":{"state":{"work_id":"9bf7e268-b9d5-4702-bb0a-14a1a4cd49b4","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":13,"external_cited_by_count":null,"distinct_field_count":3,"first_pith_cited_at":"2019-07-22T19:52:11+00:00","last_pith_cited_at":"2026-06-29T21:32:58+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-07-03T07:13:29.936132+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":1}],"polarity_counts":[{"context_polarity":"background","n":1}],"runs":{},"summary":{},"graph":{},"authors":[]}}