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We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set $\mathcal{G}$ up to the smallest possible additive term, called the convergence rate. When the…

Statistics Theory · Mathematics 2009-09-09 Jean-Yves Audibert

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set G up to the smallest possible additive term, called the convergence rate. When the reference set…

Statistics Theory · Mathematics 2008-03-04 Jean-Yves Audibert

Common machine learning settings range from supervised tasks, where accurately labeled data is accessible, through semi-supervised and weakly-supervised tasks, where target labels are scant or noisy, to unsupervised tasks where labels are…

Machine Learning · Computer Science 2025-04-22 Yogev Kriger , Shai Fine

Many real-world optimization problems contain parameters that are unknown before deployment time, either due to stochasticity or to lack of information (e.g., demand or travel times in delivery problems). A common strategy in such cases is…

We introduce a bottleneck method for learning data representations based on information deficiency, rather than the more traditional information sufficiency. A variational upper bound allows us to implement this method efficiently. The…

Information Theory · Computer Science 2020-11-05 Pradeep Kr. Banerjee , Guido Montúfar

Algorithms in machine learning and AI do critically depend on at least three key components: (i) the risk function, which is the expectation of the loss function, (ii) the function space, which is often called the hypothesis space, and…

Machine Learning · Statistics 2026-05-08 Lena Helgerth , Andreas Christmann

Dynamic nonlinear systems exhibit distortions arising from coupled static and dynamic effects. Their intertwined nature poses major challenges for data-driven modeling. This paper presents a theoretical framework grounded in structured…

Machine Learning · Computer Science 2025-09-23 Sri Satish Krishna Chaitanya Bulusu , Mikko Sillanpää

Many of the observations we make are biased by our decisions. For instance, the demand of items is impacted by the prices set, and online checkout choices are influenced by the assortments presented. The challenge in decision-making under…

Machine Learning · Computer Science 2025-07-02 Rares Cristian , Pavithra Harsha , Georgia Perakis , Brian Quanz

In the last years decision-focused learning framework, also known as predict-and-optimize, have received increasing attention. In this setting, the predictions of a machine learning model are used as estimated cost coefficients in the…

Machine Learning · Computer Science 2022-06-20 Jayanta Mandi , Víctor Bucarey , Maxime Mulamba , Tias Guns

We consider the problem of sequential decision making under uncertainty in which the loss caused by a decision depends on the following binary observation. In competitive on-line learning, the goal is to design decision algorithms that are…

Machine Learning · Computer Science 2007-05-23 Vladimir Vovk

We derive novel concentration inequalities that bound the statistical error for a large class of stochastic optimization problems, focusing on the case of unbounded objective functions. Our derivations utilize the following key tools: 1) A…

Machine Learning · Statistics 2026-01-01 Jeremiah Birrell

This paper addresses the problem of stochastic optimization with decision-dependent uncertainty, a class of problems where the probability distribution of the uncertain parameters is influenced by the decision-maker's actions. While recent…

Optimization and Control · Mathematics 2025-09-12 John Cotrina , Gonzalo Flores , David Salas , Anton Svensson

Decision analysis deals with modeling and enhancing decision processes. A principal challenge in improving behavior is in obtaining a transparent description of existing behavior in the first place. In this paper, we develop an expressive,…

Machine Learning · Statistics 2023-10-31 Daniel Jarrett , Alihan Hüyük , Mihaela van der Schaar

In this work we study loss functions for learning and evaluating probability distributions over large discrete domains. Unlike classification or regression where a wide variety of loss functions are used, in the distribution learning and…

Machine Learning · Computer Science 2019-08-05 Nika Haghtalab , Cameron Musco , Bo Waggoner

Causal analysis may be affected by selection bias, which is defined as the systematic exclusion of data from a certain subpopulation. Previous work in this area focused on the derivation of identifiability conditions. We propose instead a…

Machine Learning · Statistics 2022-08-03 Marco Zaffalon , Alessandro Antonucci , Rafael Cabañas , David Huber , Dario Azzimonti

When does society eventually learn the truth, or take the correct action, via observational learning? In a general model of sequential learning over social networks, we identify a simple condition for learning dubbed excludability.…

Theoretical Economics · Economics 2024-04-05 Navin Kartik , SangMok Lee , Tianhao Liu , Daniel Rappoport

Transfer learning seeks to accelerate sequential decision-making by leveraging offline data from related agents. However, data from heterogeneous sources that differ in observed features, distributions, or unobserved confounders often…

Machine Learning · Computer Science 2025-07-10 Xueping Gong , Wei You , Jiheng Zhang

Very often features come with their own vectorial descriptions which provide detailed information about their properties. We refer to these vectorial descriptions as feature side-information. In the standard learning scenario, input is…

Machine Learning · Computer Science 2017-03-09 Amina Mollaysa , Pablo Strasser , Alexandros Kalousis

Most data for evaluating and training recommender systems is subject to selection biases, either through self-selection by the users or through the actions of the recommendation system itself. In this paper, we provide a principled approach…

Machine Learning · Computer Science 2016-05-30 Tobias Schnabel , Adith Swaminathan , Ashudeep Singh , Navin Chandak , Thorsten Joachims

Deep Neural Networks (DNNs) often struggle with one-shot learning where we have only one or a few labeled training examples per category. In this paper, we argue that by using side information, we may compensate the missing information…

Machine Learning · Computer Science 2018-01-24 Yao-Hung Hubert Tsai , Ruslan Salakhutdinov