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In this work we investigate to which extent one can recover class probabilities within the empirical risk minimization (ERM) paradigm. The main aim of our paper is to extend existing results and emphasize the tight relations between…

Machine Learning · Computer Science 2020-07-22 Alexander Mey , Marco Loog

Following the wide-spread adoption of machine learning models in real-world applications, the phenomenon of performativity, i.e. model-dependent shifts in the test distribution, becomes increasingly prevalent. Unfortunately, since models…

Machine Learning · Statistics 2026-01-21 Ivan Kirev , Lyuben Baltadzhiev , Nikola Konstantinov

We consider the problem of empirical Bayes estimation for (multivariate) Poisson means. Existing solutions that have been shown theoretically optimal for minimizing the regret (excess risk over the Bayesian oracle that knows the prior) have…

Statistics Theory · Mathematics 2023-07-06 Soham Jana , Yury Polyanskiy , Anzo Teh , Yihong Wu

We study a class of iterated empirical risk minimization (ERM) procedures in which two successive ERMs are performed on the same dataset, and the predictions of the first estimator enter as an argument in the loss function of the second.…

Machine Learning · Statistics 2026-02-02 Hugo Cui , Yue M. Lu

Designing sample-efficient and computationally feasible reinforcement learning (RL) algorithms is particularly challenging in environments with large or infinite state and action spaces. In this paper, we advance this effort by presenting…

Machine Learning · Computer Science 2024-10-04 Zakaria Mhammedi

Motivated by the prevailing paradigm of using unsupervised learning for efficient exploration in reinforcement learning (RL) problems [tang2017exploration,bellemare2016unifying], we investigate when this paradigm is provably efficient. We…

Machine Learning · Computer Science 2020-12-02 Fei Feng , Ruosong Wang , Wotao Yin , Simon S. Du , Lin F. Yang

Large Reasoning Models (LRMs) have demonstrated remarkable performance on complex tasks but suffer from high computational costs and latency. While selective thinking strategies improve efficiency by routing easy queries to non-thinking…

Artificial Intelligence · Computer Science 2026-02-02 Chengyao Yu , Hao Zeng , Youxin Zhu , Jianguo Huang , Huajun Zeng , Bingyi Jing

Reinforcement learning (RL) is a fundamental framework for sequential decision-making, in which an agent learns an optimal policy through interactions with an unknown environment. In settings with function approximation, many existing RL…

Machine Learning · Computer Science 2026-05-05 Ruiquan Huang , Donghao Li , Yingbin Liang , Jing Yang

Empirical risk minimization (ERM) is a fundamental learning rule for statistical learning problems where the data is generated according to some unknown distribution $\mathsf{P}$ and returns a hypothesis $f$ chosen from a fixed class…

Machine Learning · Computer Science 2014-11-25 Nishant A. Mehta , Robert C. Williamson

Multi-distribution or collaborative learning involves learning a single predictor that works well across multiple data distributions, using samples from each during training. Recent research on multi-distribution learning, focusing on…

Machine Learning · Computer Science 2024-09-27 Kasper Green Larsen , Omar Montasser , Nikita Zhivotovskiy

We study risk-sensitive reinforcement learning in finite discounted MDPs with recursive entropic risk measures (ERM), where the risk parameter $\beta \neq 0$ controls the agent's risk attitude: $\beta>0$ for risk-averse and $\beta<0$ for…

Machine Learning · Computer Science 2026-05-20 Oliver Mortensen , Mohammad Sadegh Talebi

Robust learning in expressive languages with real-world data continues to be a challenging task. Numerous conventional methods appeal to heuristics without any assurances of robustness. While probably approximately correct (PAC) Semantics…

Artificial Intelligence · Computer Science 2021-09-08 Alexander P. Rader , Ionela G. Mocanu , Vaishak Belle , Brendan Juba

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

Empirical Risk Minimization (ERM) is a foundational framework for supervised learning but primarily optimizes average-case performance, often neglecting fairness and robustness considerations. Tilted Empirical Risk Minimization (TERM)…

Machine Learning · Statistics 2025-09-19 Yigit E. Yildirim , Samet Demir , Zafer Dogan

Large Language Models (LLMs) struggle with reliable mathematical reasoning, and current verification methods are often computationally expensive. This paper introduces the Energy Outcome Reward Model (EORM), a highly efficient, lightweight…

We propose a general theorem providing upper bounds for the risk of an empirical risk minimizer (ERM).We essentially focus on the binary classification framework. We extend Tsybakov's analysis of the risk of an ERM under margin type…

Statistics Theory · Mathematics 2016-08-14 Pascal Massart , Élodie Nédélec

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

We study the intrinsic limitations of sequential convex optimization through the lens of feedback information theory. In the oracle model of optimization, an algorithm queries an {\em oracle} for noisy information about the unknown…

Information Theory · Computer Science 2011-09-12 Maxim Raginsky , Alexander Rakhlin

Empirical risk minimization (ERM) incentivizes models to exploit shortcuts, i.e., spurious correlations between input attributes and labels that are prevalent in the majority of the training data but unrelated to the task at hand. This…

Machine Learning · Computer Science 2025-07-09 Michalis Korakakis , Andreas Vlachos , Adrian Weller

Empirical risk minimization (ERM), with proper loss function and regularization, is the common practice of supervised classification. In this paper, we study training arbitrary (from linear to deep) binary classifier from only unlabeled (U)…

Machine Learning · Statistics 2019-03-13 Nan Lu , Gang Niu , Aditya Krishna Menon , Masashi Sugiyama