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A Unified Semismooth Newton Approach to Multitask and Multivariate Square-Root Lasso Problems

NeurIPS 2026 · Learning theory and algorithms › Matrix and tensor methods · approach: Nonconvex low-rank and sparse optimization

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Proposes a semismooth Newton framework for computing multitask and multivariate square-root Lasso estimators, which have scale-free tuning but nonsmooth loss and penalty.

Problem

Computing high-dimensional square-root Lasso estimators with multiple responses at large scale is hard because both the loss and penalty terms are nonsmooth.

Approach

A unified computational framework based on semismooth Newton methods that applies universally to multitask and multivariate square-root Lasso problems, exploiting second-order information despite nonsmoothness in both terms.

Experimental setup

Builds on: square-root Lasso

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