Range Penalization: Theoretical Insights with Applications in Federated Learning

• URL: http://arxiv.org/abs/2606.10916v1
• Date: Tue, 09 Jun 2026 14:26:28 GMT
• Title: Range Penalization: Theoretical Insights with Applications in Federated Learning
• Abstract summary: We introduce range regularization for federated learning with linear systematic components to enhance statistical accuracy.<n>Our approach identifies features with shared weights across different clients and adaptively clusters the weights of personalized features at extreme values.<n>We develop new proof techniques for the nonasymptotic analysis of statistical accuracy and faithful pattern recovery.
• Score: 4.955027506950935
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper introduces range regularization for federated learning with linear systematic components to enhance statistical accuracy and induce cross-client regularity conducive to quantization, coding, and resource efficiency. Our approach identifies features with shared weights across different clients and adaptively clusters the weights of personalized features at extreme values, a process we refer to as polar clustering. Theoretical analysis of the associated estimators poses significant challenges due to the seminorm nature and non-decomposability of the regularizer. We develop new proof techniques for the nonasymptotic analysis of statistical accuracy and faithful pattern recovery. Moreover, a fast optimization algorithm that leverages varying degrees of local strong convexity is proposed to reduce iteration complexity. Experiments support the efficacy and efficiency of the proposed approach.

Related papers

• Adaptive Estimation and Inference in Semi-parametric Heterogeneous Clustered Multitask Learning via Neyman Orthogonality [9.091986429838117]
  We study clustered multitask learning in a semiparametric setting where tasks share a latent cluster structure in their target parameters but exhibit heterogeneous, potentially infinite-dimensional nuisance components.<n>Our framework integrates Neyman-orthogonal losses with data-driven pairwise fusion penalties.<n> Empirically, we show that the proposed method consistently outperforms strong baselines in various simulation setups.
  arXiv  Detail & Related papers  (2026-05-03T14:43:17Z)
• Towards regularized learning from functional data with covariate shift [3.072411352294816]
  This paper investigates a general regularization framework for unsupervised domain adaptation in vector-valued regression.<n>By restricting the hypothesis space, we develop a practical operator learning algorithm capable of handling functional outputs.
  arXiv  Detail & Related papers  (2026-01-28T20:30:05Z)
• Neural Optimal Transport Meets Multivariate Conformal Prediction [58.43397908730771]
  We propose a framework for conditional vectorile regression (CVQR)<n>CVQR combines neural optimal transport with quantized optimization, and apply it to predictions.
  arXiv  Detail & Related papers  (2025-09-29T19:50:19Z)
• Hadamard-Riemannian Optimization for Margin-Variance Ensemble [0.0]
  This paper introduces a novel ensemble learning framework that explicitly incorporates margin variance into the loss function.<n>Our method jointly optimize the negative expected margin and its variance, leading to enhanced robustness and improved generalization performance.
  arXiv  Detail & Related papers  (2025-09-12T12:28:39Z)
• Stochastic Optimization with Optimal Importance Sampling [49.484190237840714]
  We propose an iterative-based algorithm that jointly updates the decision and the IS distribution without requiring time-scale separation between the two.<n>Our method achieves the lowest possible variable variance and guarantees global convergence under convexity of the objective and mild assumptions on the IS distribution family.
  arXiv  Detail & Related papers  (2025-04-04T16:10:18Z)
• Regularization for Adversarial Robust Learning [18.46110328123008]
  We develop a novel approach to adversarial training that integrates $phi$-divergence regularization into the distributionally robust risk function. This regularization brings a notable improvement in computation compared with the original formulation. We validate our proposed method in supervised learning, reinforcement learning, and contextual learning and showcase its state-of-the-art performance against various adversarial attacks.
  arXiv  Detail & Related papers  (2024-08-19T03:15:41Z)
• Generalization Bounds of Surrogate Policies for Combinatorial Optimization Problems [53.03951222945921]
  We analyze smoothed (perturbed) policies, adding controlled random perturbations to the direction used by the linear oracle.<n>Our main contribution is a generalization bound that decomposes the excess risk into perturbation bias, statistical estimation error, and optimization error.<n>We illustrate the scope of the results on applications such as vehicle scheduling, highlighting how smoothing enables both tractable training and controlled generalization.
  arXiv  Detail & Related papers  (2024-07-24T12:00:30Z)
• Out-of-distribution robustness for multivariate analysis via causal regularisation [4.487663958743944]
  We propose a regularisation strategy rooted in causality that ensures robustness against distribution shifts.<n>Building upon the anchor regression framework, we demonstrate how incorporating a straightforward regularisation term into the loss function of classical algorithms.<n>Our framework allows users to efficiently verify the compatibility of a loss function with the regularisation strategy.
  arXiv  Detail & Related papers  (2024-03-04T09:21:10Z)
• Likelihood Ratio Confidence Sets for Sequential Decision Making [51.66638486226482]
  We revisit the likelihood-based inference principle and propose to use likelihood ratios to construct valid confidence sequences. Our method is especially suitable for problems with well-specified likelihoods. We show how to provably choose the best sequence of estimators and shed light on connections to online convex optimization.
  arXiv  Detail & Related papers  (2023-11-08T00:10:21Z)
• Distributionally Robust Model-based Reinforcement Learning with Large State Spaces [55.14361269378122]
  Three major challenges in reinforcement learning are the complex dynamical systems with large state spaces, the costly data acquisition processes, and the deviation of real-world dynamics from the training environment deployment. We study distributionally robust Markov decision processes with continuous state spaces under the widely used Kullback-Leibler, chi-square, and total variation uncertainty sets. We propose a model-based approach that utilizes Gaussian Processes and the maximum variance reduction algorithm to efficiently learn multi-output nominal transition dynamics.
  arXiv  Detail & Related papers  (2023-09-05T13:42:11Z)
• Multiplicative noise and heavy tails in stochastic optimization [62.993432503309485]
  empirical optimization is central to modern machine learning, but its role in its success is still unclear. We show that it commonly arises in parameters of discrete multiplicative noise due to variance. A detailed analysis is conducted in which we describe on key factors, including recent step size, and data, all exhibit similar results on state-of-the-art neural network models.
  arXiv  Detail & Related papers  (2020-06-11T09:58:01Z)

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.