Renet: Principled and Efficient Relaxation for the Elastic Net via Dynamic Objective Selection

• URL: http://arxiv.org/abs/2602.11107v1
• Date: Wed, 11 Feb 2026 18:22:59 GMT
• Title: Renet: Principled and Efficient Relaxation for the Elastic Net via Dynamic Objective Selection
• Authors: Albert Dorador,
• Abstract summary: We introduce Renet, a principled generalization of the Relaxed Lasso to the Elastic Net family of estimators.<n>We show that Renet consistently outperforms the standard Elastic Net in high-dimensional, low signal-to-noise ratio and high-multicolline regimes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We introduce Renet, a principled generalization of the Relaxed Lasso to the Elastic Net family of estimators. While, on the one hand, $\ell_1$-regularization is a standard tool for variable selection in high-dimensional regimes and, on the other hand, the $\ell_2$ penalty provides stability and solution uniqueness through strict convexity, the standard Elastic Net nevertheless suffers from shrinkage bias that frequently yields suboptimal prediction accuracy. We propose to address this limitation through a framework called \textit{relaxation}. Existing relaxation implementations rely on naive linear interpolations of penalized and unpenalized solutions, which ignore the non-linear geometry that characterizes the entire regularization path and risk violating the Karush-Kuhn-Tucker conditions. Renet addresses these limitations by enforcing sign consistency through an adaptive relaxation procedure that dynamically dispatches between convex blending and efficient sub-path refitting. Furthermore, we identify and formalize a unique synergy between relaxation and the ``One-Standard-Error'' rule: relaxation serves as a robust debiasing mechanism, allowing practitioners to leverage the parsimony of the 1-SE rule without the traditional loss in predictive fidelity. Our theoretical framework incorporates automated stability safeguards for ultra-high dimensional regimes and is supported by a comprehensive benchmarking suite across 20 synthetic and real-world datasets, demonstrating that Renet consistently outperforms the standard Elastic Net and provides a more robust alternative to the Adaptive Elastic Net in high-dimensional, low signal-to-noise ratio and high-multicollinearity regimes. By leveraging an adaptive solver backend, Renet delivers these statistical gains while offering a computational profile that remains competitive with state-of-the-art coordinate descent implementations.

Related papers

• Stability and Generalization of Push-Sum Based Decentralized Optimization over Directed Graphs [55.77845440440496]
  Push-based decentralized communication enables optimization over communication networks, where information exchange may be asymmetric.<n>We develop a unified uniform-stability framework for the Gradient Push (SGP) algorithm.<n>A key technical ingredient is an imbalance-aware generalization bound through two quantities.
  arXiv  Detail & Related papers  (2026-02-24T05:32:03Z)
• Unifying Stable Optimization and Reference Regularization in RLHF [64.16830602324345]
  This paper introduces a unified regularization approach that balances objectives of preventing reward hacking and maintaining stable policy updates.<n>Our simple yet principled alignment objective yields a weighted supervised fine-tuning loss with a superior trade-off, which demonstrably improves both alignment results and implementation complexity.
  arXiv  Detail & Related papers  (2026-02-12T03:31:19Z)
• MAESTRO: Meta-learning Adaptive Estimation of Scalarization Trade-offs for Reward Optimization [56.074760766965085]
  Group-Relative Policy Optimization has emerged as an efficient paradigm for aligning Large Language Models (LLMs)<n>We propose MAESTRO, which treats reward scalarization as a dynamic latent policy, leveraging the model's terminal hidden states as a semantic bottleneck.<n>We formulate this as a contextual bandit problem within a bi-level optimization framework, where a lightweight Conductor network co-evolves with the policy by utilizing group-relative advantages as a meta-reward signal.
  arXiv  Detail & Related papers  (2026-01-12T05:02:48Z)
• Beyond Additivity: Sparse Isotonic Shapley Regression toward Nonlinear Explainability [0.0]
  We introduce Sparse Isotonic Shapley Regression (SISR), a unified nonlinear explanation framework.<n>SISR learns a monotonic transformation to restore additivity--obviating the need for a closed-form specification--and enforces an L0 sparsity constraint on the Shapley vector.<n>SISR stabilizes attributions across payoff schemes, correctly filters irrelevant features while standard Shapley values suffer severe rank and sign distortions.
  arXiv  Detail & Related papers  (2025-12-02T08:34:43Z)
• Optimal Regularization Under Uncertainty: Distributional Robustness and Convexity Constraints [9.77322868877488]
  We introduce a framework for distributionally robust optimal regularization.<n>We show how the resulting robust regularizers interpolate between computation of the training distribution and uniform priors.
  arXiv  Detail & Related papers  (2025-10-03T19:35:38Z)
• Resilient Constrained Reinforcement Learning [87.4374430686956]
  We study a class of constrained reinforcement learning (RL) problems in which multiple constraint specifications are not identified before study. It is challenging to identify appropriate constraint specifications due to the undefined trade-off between the reward training objective and the constraint satisfaction. We propose a new constrained RL approach that searches for policy and constraint specifications together.
  arXiv  Detail & Related papers  (2023-12-28T18:28:23Z)
• Outlier-robust neural network training: variation regularization meets trimmed loss to prevent functional breakdown [2.5628953713168685]
  We tackle the challenge of outlier-robust predictive modeling using highly expressive neural networks.<n>Our approach integrates two key components: (1) a transformed trimmed loss (TTL), and (2) higher-order variation regularization (HOVR), which imposes smoothness constraints on the prediction function.
  arXiv  Detail & Related papers  (2023-08-04T12:57:13Z)
• Provably tuning the ElasticNet across instances [53.0518090093538]
  We consider the problem of tuning the regularization parameters of Ridge regression, LASSO, and the ElasticNet across multiple problem instances. Our results are the first general learning-theoretic guarantees for this important class of problems.
  arXiv  Detail & Related papers  (2022-07-20T21:22:40Z)
• Towards Understanding Generalization via Decomposing Excess Risk Dynamics [13.4379473119565]
  We analyze the generalization dynamics to derive algorithm-dependent bounds, e.g., stability. Inspired by the observation that neural networks show a slow convergence rate when fitting noise, we propose decomposing the excess risk dynamics. Under the decomposition framework, the new bound accords better with the theoretical and empirical evidence compared to the stability-based bound and uniform convergence bound.
  arXiv  Detail & Related papers  (2021-06-11T03:42:45Z)
• Improve Generalization and Robustness of Neural Networks via Weight Scale Shifting Invariant Regularizations [52.493315075385325]
  We show that a family of regularizers, including weight decay, is ineffective at penalizing the intrinsic norms of weights for networks with homogeneous activation functions. We propose an improved regularizer that is invariant to weight scale shifting and thus effectively constrains the intrinsic norm of a neural network.
  arXiv  Detail & Related papers  (2020-08-07T02:55:28Z)
• Sparse Identification of Nonlinear Dynamical Systems via Reweighted $\ell_1$-regularized Least Squares [62.997667081978825]
  This work proposes an iterative sparse-regularized regression method to recover governing equations of nonlinear systems from noisy state measurements. The aim of this work is to improve the accuracy and robustness of the method in the presence of state measurement noise.
  arXiv  Detail & Related papers  (2020-05-27T08:30:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.