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This paper introduces adaptive Bregman proximal gradient algorithms for solving convex composite minimization problems without relying on global relative smoothness or strong convexity assumptions. Building upon recent advances in adaptive…

Optimization and Control · Mathematics 2025-08-05 Hongjia Ou , Puya Latafat , Andreas Themelis

In this paper, we develop a wide class Mirror Descent (MD) algorithms, which play a key role in machine learning. For this purpose we formulated the constrained optimization problem, in which we exploits the Bregman divergence with the…

Machine Learning · Statistics 2025-06-18 Andrzej Cichocki

This work addresses the problem of error concealment in video transmission systems over noisy channels employing Bregman divergences along with regularization. Error concealment intends to improve the effects of disturbances at the…

Computer Vision and Pattern Recognition · Computer Science 2016-11-11 Alessandra M. Coelho , Vania V. Estrela , Felipe P. do Carmo , Sandro R. Fernandes

This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to…

Machine Learning · Statistics 2018-07-17 Arnaud Dessein , Nicolas Papadakis , Jean-Luc Rouas

In this paper we introduce two conceptual algorithms for minimising abstract convex functions. Both algorithms rely on solving a proximal-type subproblem with an abstract Bregman distance based proximal term. We prove their convergence when…

Optimization and Control · Mathematics 2026-01-09 Reinier Díaz Millán , Julien Ugon

Preference-based reinforcement learning (PbRL) promises to learn a complex reward function with binary human preference. However, such human-in-the-loop formulation requires considerable human effort to assign preference labels to segment…

Machine Learning · Computer Science 2023-07-20 Yachen Kang , Li He , Jinxin Liu , Zifeng Zhuang , Donglin Wang

This letter investigates the convergence and concentration properties of the Stochastic Mirror Descent (SMD) algorithm utilizing biased stochastic subgradients. We establish the almost sure convergence of the algorithm's iterates under the…

Optimization and Control · Mathematics 2024-07-09 Anik Kumar Paul , Arun D Mahindrakar , Rachel K Kalaimani

Bayesian methods are appealing in their flexibility in modeling complex data and ability in capturing uncertainty in parameters. However, when Bayes' rule does not result in tractable closed-form, most approximate inference algorithms lack…

Machine Learning · Computer Science 2016-05-09 Bo Dai , Niao He , Hanjun Dai , Le Song

The Proximal Point Method (PPM) (Rockafellar, 1976) is a fundamental tool for nonsmooth convex optimization. However, its convergence is not linear under general convexity in the absence of strong convexity or other structural assumptions.…

Optimization and Control · Mathematics 2026-04-06 Hanmin Li , Kaja Gruntkowska , Peter Richtárik

In this paper, we generalize the notions of centroids and barycenters to the broad class of information-theoretic distortion measures called Bregman divergences. Bregman divergences are versatile, and unify quadratic geometric distances…

Computational Geometry · Computer Science 2007-11-22 Frank Nielsen , Richard Nock

This paper studies the convergence of the mirror descent algorithm for finite horizon stochastic control problems with measure-valued control processes. The control objective involves a convex regularisation function, denoted as $h$, with…

Optimization and Control · Mathematics 2025-08-22 Bekzhan Kerimkulov , David Šiška , Łukasz Szpruch , Yufei Zhang

Classical linear metric learning methods have recently been extended along two distinct lines: deep metric learning methods for learning embeddings of the data using neural networks, and Bregman divergence learning approaches for extending…

Machine Learning · Computer Science 2020-05-07 Kubra Cilingir , Rachel Manzelli , Brian Kulis

Restricted Boltzmann Machines (RBMs) offer a versatile architecture for unsupervised machine learning that can in principle approximate any target probability distribution with arbitrary accuracy. However, the RBM model is usually not…

Machine Learning · Computer Science 2022-09-27 Lennart Dabelow , Masahito Ueda

In this paper we study a nonlinear dual space preconditioning approach for the relaxed Proximal Point Algorithm (PPA) with application to monotone and relatively cohypomonotone inclusions, called anisotropic PPA. The algorithm is an…

Optimization and Control · Mathematics 2025-12-30 Emanuel Laude , Panagiotis Patrinos

In this paper, we study the design and analysis of a class of efficient algorithms for computing the Gromov-Wasserstein (GW) distance tailored to large-scale graph learning tasks. Armed with the Luo-Tseng error bound…

Machine Learning · Computer Science 2022-12-15 Jiajin Li , Jianheng Tang , Lemin Kong , Huikang Liu , Jia Li , Anthony Man-Cho So , Jose Blanchet

Many learning algorithms such as kernel machines, nearest neighbors, clustering, or anomaly detection, are based on the concept of 'distance' or 'similarity'. Before similarities are used for training an actual machine learning model, we…

Recent advances in machine learning have led to increased interest in reproducing kernel Banach spaces (RKBS) as a more general framework that extends beyond reproducing kernel Hilbert spaces (RKHS). These works have resulted in the…

Machine Learning · Computer Science 2024-11-19 Akash Kumar , Mikhail Belkin , Parthe Pandit

Low rank approximation is a commonly occurring problem in many computer vision and machine learning applications. There are two common ways of optimizing the resulting models. Either the set of matrices with a given rank can be explicitly…

Computer Vision and Pattern Recognition · Computer Science 2019-07-24 Marcus Valtonen Örnhag , Carl Olsson , Anders Heyden

Ill-posed linear inverse problems appear in many scientific setups, and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection…

Optimization and Control · Mathematics 2021-08-10 Tom Tirer , Raja Giryes

In the present work, we present numerical results for an iterative method for solving an optimal control problem with inequality contraints. The method is based on generalized Bregman distances. Under a combination of a source condition and…

Optimization and Control · Mathematics 2016-06-07 Frank Pörner