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We study the cyclic relaxed Douglas-Rachford algorithm for possibly nonconvex, and inconsistent feasibility problems. This algorithm can be viewed as a convex relaxation between the cyclic Douglas-Rachford algorithm first introduced by…

Optimization and Control · Mathematics 2026-05-06 Thi Lan Dinh , G. S. Matthijs Jansen , D. Russell Luke

We introduce and study a geometric modification of the Douglas-Rach\-ford method called the Circumcentered-Douglas-Rachford method. This method iterates by taking the intersection of bisectors of reflection steps for solving certain classes…

Optimization and Control · Mathematics 2020-08-11 Roger Behling , Jose Yunier Bello Cruz , Luiz-Rafael Santos

The Douglas--Rachford algorithm is a classic splitting method for finding a zero of the sum of two maximal monotone operators. It has also been applied to settings that involve one weakly and one strongly monotone operator. In this work, we…

Optimization and Control · Mathematics 2025-11-07 Jan Harold Alcantara , Akiko Takeda

We study federated learning (FL) -- especially cross-silo FL -- with non-convex loss functions and data from people who do not trust the server or other silos. In this setting, each silo (e.g. hospital) must protect the privacy of each…

Machine Learning · Computer Science 2023-06-27 Andrew Lowy , Ali Ghafelebashi , Meisam Razaviyayn

Federated learning (FL) has been recognized as a rapidly growing research area, where the model is trained over massively distributed clients under the orchestration of a parameter server (PS) without sharing clients' data. This paper…

Machine Learning · Computer Science 2024-04-04 Yiwei Li , Chien-Wei Huang , Shuai Wang , Chong-Yung Chi , Tony Q. S. Quek

Selecting an optimal subset of features or instances under an information theoretic criterion has become an effective preprocessing strategy for reducing data complexity while preserving essential information. This study investigates two…

Optimization and Control · Mathematics 2025-08-25 Taotao He , Jun Luo , Junkai Zhao

In this paper, to effectively prevent information leakage, we propose a novel framework based on the concept of differential privacy (DP), in which artificial noises are added to the parameters at the clients side before aggregating,…

Machine Learning · Computer Science 2019-11-11 Kang Wei , Jun Li , Ming Ding , Chuan Ma , Howard H. Yang , Farokhi Farhad , Shi Jin , Tony Q. S. Quek , H. Vincent Poor

User-level differentially private stochastic convex optimization (DP-SCO) has garnered significant attention due to the paramount importance of safeguarding user privacy in modern large-scale machine learning applications. Current methods,…

Machine Learning · Computer Science 2025-02-14 Badih Ghazi , Ravi Kumar , Daogao Liu , Pasin Manurangsi

We study two dual settings of information processing. Let $ \mathsf{Y} \rightarrow \mathsf{X} \rightarrow \mathsf{W} $ be a Markov chain with fixed joint probability mass function $ \mathsf{P}_{\mathsf{X}\mathsf{Y}} $ and a mutual…

Information Theory · Computer Science 2021-10-05 Michael Dikshtein , Shlomo Shamai

The Douglas-Rachford and Peaceman-Rachford algorithms have been successfully employed to solve convex optimization problems, or more generally find zeros of monotone inclusions. Recently, the behaviour of these methods in the inconsistent…

Optimization and Control · Mathematics 2024-05-28 Regina S. Burachik , Bethany I. Caldwell , C. Yalçın Kaya , Walaa M. Moursi , Matthew Saurette

Federated Learning with client-level differential privacy (DP) provides a promising framework for collaboratively training models while rigorously protecting clients' privacy. However, classic approaches like DP-FedAvg struggle when clients…

Cryptography and Security · Computer Science 2026-02-10 Jiahao Xu , Rui Hu , Olivera Kotevska

rdering of regression or classification coefficients occurs in many real-world applications. Fused Lasso exploits this ordering by explicitly regularizing the differences between neighboring coefficients through an $\ell_1$ norm…

Computation · Statistics 2010-06-29 Gui-Bo Ye , Xiaohui Xie

Dual decomposition approaches in nonconvex optimization may suffer from a duality gap. This poses a challenge when applying them directly to nonconvex problems such as MAP-inference in a Markov random field (MRF) with continuous state…

Optimization and Control · Mathematics 2022-05-17 Hartmut Bauermeister , Emanuel Laude , Thomas Möllenhoff , Michael Moeller , Daniel Cremers

The Douglas--Rachford and Peaceman--Rachford splitting methods are common choices for temporal discretizations of evolution equations. In this paper we combine these methods with spatial discretizations fulfilling some easily verifiable…

Numerical Analysis · Mathematics 2016-05-10 Eskil Hansen , Erik Henningsson

In spite that Federated Learning (FL) is well known for its privacy protection when training machine learning models among distributed clients collaboratively, recent studies have pointed out that the naive FL is susceptible to gradient…

Cryptography and Security · Computer Science 2021-01-13 Yao Fu , Yipeng Zhou , Di Wu , Shui Yu , Yonggang Wen , Chao Li

In this paper we propose \texttt{GIFAIR-FL}: a framework that imposes \textbf{G}roup and \textbf{I}ndividual \textbf{FAIR}ness to \textbf{F}ederated \textbf{L}earning settings. By adding a regularization term, our algorithm penalizes the…

Machine Learning · Computer Science 2023-07-04 Xubo Yue , Maher Nouiehed , Raed Al Kontar

Our interest lies in developing some efficient methods for minimizing the sum of two geodesically convex functions on Hadamard manifolds, with the aim to enhance the convergence of the Douglas-Rachford algorithm in Hadamard manifolds.…

Optimization and Control · Mathematics 2026-02-17 D. R. Sahu , Shikher Sharma , Pankaj Gautam

For solving the large-scale linear system by iteration methods, we utilize the Petrov-Galerkin conditions and relaxed greedy index selection technique and provide two relaxed greedy deterministic row (RGDR) and column (RGDC) iterative…

Numerical Analysis · Mathematics 2022-08-12 Nian-Ci Wu , Ling-Xia Cui , Qian Zuo

The problem of distributed representation learning is one in which multiple sources of information $X_1,\ldots,X_K$ are processed separately so as to learn as much information as possible about some ground truth $Y$. We investigate this…

Machine Learning · Statistics 2019-04-02 Inaki Estella Aguerri , Abdellatif Zaidi

The Iterative Markovian Fitting (IMF) procedure, which iteratively projects onto the space of Markov processes and the reciprocal class, successfully solves the Schr\"odinger Bridge (SB) problem. However, an efficient practical…