arXiv:2502. 00753v4 Announce Type: replace-cross Abstract: Smoothness is crucial for attaining fast rates in first-order optimization.
By Dingzhi Yu, Wei Jiang, Hongyi Tao, Yuanyu Wan, Lijun Zhang
The paper investigates how the choice of geometry in online mirror descent affects performance, particularly when loss gradients are sparse. It introduces randomized block‑norm mirror maps that interpolate between Euclidean and entropic geometries, achieving polynomial‑in‑dimension regret improvements over standard methods for various convex sets. The authors also demonstrate that naive alternation between mirror maps can lead to linear regret and propose a Hedge‑based meta‑algorithm that competes with the best mirror map in a finite portfolio, achieving near‑optimal regret for random block geometries.
By Swati Gupta, Jai Moondra, Mohit Singh
arXiv:2610. 12328v1 Announce Type: new Abstract: We consider stochastic nonsmooth nonconvex composite optimization, which includes several important problems such as constrained optimization and the regularized training of neural networks.
By Mingyi Li, Taira Tsuchiya, Kenji Yamanishi
arXiv:2606. 11431v1 Announce Type: new Abstract: Mirror Descent (MD) extends Gradient Descent (GD) beyond Euclidean geometry and has recently reappeared as a lens for KL-regularized policy optimization in reinforcement learning and LLM post-training.
By Shira Vansover-Hager, Matan Schliserman, Ofir Schlisselberg, Tomer Koren
arXiv:2602. 23116v3 Announce Type: replace Abstract: We consider the problem of regularized best-response max-regret minimization in online RLHF under general preferences and bandit feedback.
By Junghyun Lee, Minju Hong, Kwang-Sung Jun, Chulhee Yun, Se-Young Yun
arXiv:2608. 22834v2 Announce Type: replace-cross Abstract: We derive convergence guarantees for mirror descent and proximal mirror descent with a logarithmic barrier as the distance-generating function.
By Alberto De Marchi, Yura Malitsky, Adrien B. Taylor