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Empirical Risk Minimization (ERM) based machine learning algorithms have suffered from weak generalization performance on data obtained from out-of-distribution (OOD). To address this problem, Invariant Risk Minimization (IRM) objective was…

Machine Learning · Computer Science 2021-03-25 Jun-Hyun Bae , Inchul Choi , Minho Lee

The empirical risk minimization (ERM) problem with relative entropy regularization (ERM-RER) is investigated under the assumption that the reference measure is a $\sigma$-finite measure, and not necessarily a probability measure. Under this…

Statistics Theory · Mathematics 2024-04-09 Samir M. Perlaza , Gaetan Bisson , Iñaki Esnaola , Alain Jean-Marie , Stefano Rini

Empirical risk minimization (ERM) can be computationally expensive, with standard solvers scaling poorly even in the convex setting. We propose a novel lossless compression framework for convex ERM based on color refinement, extending prior…

Optimization and Control · Mathematics 2026-02-03 Bryan Zhu , Ziang Chen

We develop a learning principle and an efficient algorithm for batch learning from logged bandit feedback. This learning setting is ubiquitous in online systems (e.g., ad placement, web search, recommendation), where an algorithm makes a…

Machine Learning · Computer Science 2015-05-22 Adith Swaminathan , Thorsten Joachims

In this work, we study the weighted empirical risk minimization (weighted ERM) schema, in which an additional data-dependent weight function is incorporated when the empirical risk function is being minimized. We show that under a general…

Machine Learning · Computer Science 2025-01-07 Yikai Zhang , Jiahe Lin , Fengpei Li , Songzhu Zheng , Anant Raj , Anderson Schneider , Yuriy Nevmyvaka

Many modern computational approaches to classical problems in quantitative finance are formulated as empirical loss minimization (ERM), allowing direct applications of classical results from statistical machine learning. These methods,…

Machine Learning · Statistics 2022-09-27 A. Max Reppen , H. Mete Soner

In a wide range of statistical learning problems such as ranking, clustering or metric learning among others, the risk is accurately estimated by $U$-statistics of degree $d\geq 1$, i.e. functionals of the training data with low variance…

Machine Learning · Statistics 2019-01-25 Stéphan Clémençon , Aurélien Bellet , Igor Colin

The imitation learning of self-driving vehicle policies through behavioral cloning is often carried out in an open-loop fashion, ignoring the effect of actions to future states. Training such policies purely with Empirical Risk Minimization…

Machine Learning · Computer Science 2022-10-12 Eesha Kumar , Yiming Zhang , Stefano Pini , Simon Stent , Ana Ferreira , Sergey Zagoruyko , Christian S. Perone

We develop a rigorous framework for deterministic coreset construction in empirical risk minimization (ERM). Our central contribution is the Adaptive Deterministic Uniform-Weight Trimming (ADUWT) algorithm, which constructs a coreset by…

Machine Learning · Statistics 2025-08-27 Faruk Alpay , Taylan Alpay

Optimizing machine learning algorithms that are used to solve the objective function has been of great interest. Several approaches to optimize common algorithms, such as gradient descent and stochastic gradient descent, were explored. One…

Machine Learning · Computer Science 2022-10-06 Hilal AlQuabeh , Farha AlBreiki , Dilshod Azizov

We give a general result concerning the rates of convergence of penalized empirical risk minimizers (PERM) in the regression model. Then, we consider the problem of agnostic learning of the regression, and give in this context an oracle…

Statistics Theory · Mathematics 2008-10-30 S. Gaïffas , G. Lecué

The multi-armed bandit (MAB) problem is a ubiquitous decision-making problem that exemplifies exploration-exploitation tradeoff. Standard formulations exclude risk in decision making. Risknotably complicates the basic reward-maximising…

Machine Learning · Computer Science 2021-05-17 Ming Liang Ang , Eloise Y. Y. Lim , Joel Q. L. Chang

Developing simple, sample-efficient learning algorithms for robust classification is a pressing issue in today's tech-dominated world, and current theoretical techniques requiring exponential sample complexity and complicated improper…

Machine Learning · Computer Science 2023-02-07 Robi Bhattacharjee , Max Hopkins , Akash Kumar , Hantao Yu , Kamalika Chaudhuri

We consider the random design regression model with square loss. We propose a method that aggregates empirical minimizers (ERM) over appropriately chosen random subsets and reduces to ERM in the extreme case, and we establish sharp oracle…

Statistics Theory · Mathematics 2017-07-04 Alexander Rakhlin , Karthik Sridharan , Alexandre B. Tsybakov

In real-world applications, the distribution of the data, and our goals, evolve over time. The prevailing theoretical framework for studying machine learning, namely probably approximately correct (PAC) learning, largely ignores time. As a…

Machine Learning · Statistics 2025-01-31 Ashwin De Silva , Rahul Ramesh , Rubing Yang , Siyu Yu , Joshua T Vogelstein , Pratik Chaudhari

The field of Machine Learning has changed significantly since the 1970s. However, its most basic principle, Empirical Risk Minimization (ERM), remains unchanged. We propose Functional Risk Minimization~(FRM), a general framework where…

Currently, machine learning plays an important role in the lives and individual activities of numerous people. Accordingly, it has become necessary to design machine learning algorithms to ensure that discrimination, biased views, or unfair…

Machine Learning · Statistics 2015-11-09 Kazuto Fukuchi , Jun Sakuma

The optimality and sensitivity of the empirical risk minimization problem with relative entropy regularization (ERM-RER) are investigated for the case in which the reference is a sigma-finite measure instead of a probability measure. This…

Machine Learning · Computer Science 2022-11-15 Samir M. Perlaza , Gaetan Bisson , Iñaki Esnaola , Alain Jean-Marie , Stefano Rini

We design and implement an adaptive experiment (a ``contextual bandit'') to learn a targeted treatment assignment policy, where the goal is to use a participant's survey responses to determine which charity to expose them to in a donation…

Networked data, in which every training example involves two objects and may share some common objects with others, is used in many machine learning tasks such as learning to rank and link prediction. A challenge of learning from networked…

Machine Learning · Computer Science 2017-11-23 Yuanhong Wang , Yuyi Wang , Xingwu Liu , Juhua Pu