{"ID":2850204,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.22135","arxiv_id":"2510.22135","title":"Accelerated Distance-adaptive Methods for Hölder Smooth and Convex Optimization","abstract":"This paper introduces new parameter-free first-order methods for convex optimization problems in which the objective function exhibits Hölder smoothness. Inspired by the recently proposed distance-over-gradient (DOG) technique, we propose an accelerated distance-adaptive method which achieves optimal anytime convergence rates for Hölder smooth problems without requiring prior knowledge of smoothness parameters or explicit parameter tuning. Importantly, our parameter-free approach removes the necessity of specifying target accuracy in advance, addressing a limitation found in the universal fast gradient methods (Nesterov, Yu. \\textit{Mathematical Programming}, 2015). For convex stochastic optimization, we further present a parameter-free accelerated method that eliminates the need for line-search procedures. Preliminary experimental results highlight the effectiveness of our approach on convex nonsmooth problems and its advantages over existing parameter-free or accelerated methods.","short_abstract":"This paper introduces new parameter-free first-order methods for convex optimization problems in which the objective function exhibits Hölder smoothness. Inspired by the recently proposed distance-over-gradient (DOG) technique, we propose an accelerated distance-adaptive method which achieves optimal anytime convergenc...","url_abs":"https://arxiv.org/abs/2510.22135","url_pdf":"https://arxiv.org/pdf/2510.22135v1","authors":"[\"Yijin Ren\",\"Haifeng Xu\",\"Qi Deng\"]","published":"2025-10-25T03:15:07Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}