Year: 2026
Type: preprint
Abstract: In this paper, we solve risk functional minimization problems with general losses in Banach spaces within the framework of stochastic approximation. We introduce an adaptive regularization strategy for stochastic mirror descent (SMD). Specifically, using a Schauder basis, we construct nested finite-dimensional subspaces whose dimensions adapt to the sample size $n$ to balance approximation and optimization errors. We solve each SMD subproblem over the corresponding subspace and project the stochastic subgradient onto its dual space. This yields closed-form solutions and coordinate-wise coefficient updates with low computational and storage complexity. For risk minimization in $\mathcal{L}^p$ spaces with $1
Source: arXiv (Cornell University)
Authors: Bai, Jinhui, Lu, Shuai, Shi, Lei
Institution: Fudan University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203451468