Research map / Optimization / Nonconvex and smooth optimization

Affine-invariant Cubic Newton with Weak Learners

NeurIPS 2026 · Optimization › Nonconvex and smooth optimization · approach: Acceleration and Nesterov dynamics

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's abstract only. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Proposes an affine-invariant cubic Newton variant for gradient boosting with weak learners, aiming to improve on the global O(1/(γ^12 k^2)) rate of gradient-regularized Newton boosting.

Problem

Newton-based gradient boosting works well empirically but lacks global convergence guarantees; prior gradient-regularized Newton boosting has a global O(1/(γ^12 k^2)) rate with a severe dependence on the weak gradient edge γ and does not exploit Hessian geometry.

Approach

Uses cubic Newton-style regularization that is affine-invariant, exploiting the natural Hessian geometry to obtain better dependence on the weak gradient edge than prior gradient-regularized Newton boosting. Details beyond the abstract are not available.

Experimental setup

Baselines: gradient-regularized Newton (GRN) boosting

Builds on: gradient-regularized Newton boosting

Closest papers by meaning

• Gradient Regularized Newton Boosting Trees with Global Convergence (NeurIPS 2026 · similarity 0.90)
• A Regularized Newton Method for Nonconvex Optimization with Global and Local Complexity Guarantees (NeurIPS 2025 · similarity 0.89)
• Skip the Hessian, Keep the Rates: Globalized Semismooth Newton with Lazy Hessian Updates (NeurIPS 2026 · similarity 0.88)
• Convergence Analysis of Newton's Method for Neural Networks in the Overparameterized Limit (NeurIPS 2026 · similarity 0.86)
• Provable Acceleration of Nesterov's Accelerated Gradient for Asymmetric Matrix Factorization and Linear Neural Networks (NeurIPS 2024 · similarity 0.86)
• Spectral Preconditioning for Gradient Methods on Graded Non-convex Functions (ICML 2024 · similarity 0.86)