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We consider composite loss functions for multiclass prediction comprising a proper (i.e., Fisher-consistent) loss over probability distributions and an inverse link function. We establish conditions for their (strong) convexity and explore…

Machine Learning · Computer Science 2012-06-22 Mark Reid , Robert Williamson , Peng Sun

Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However,…

Machine Learning · Computer Science 2025-03-05 Dimitris Bertsimas , Benjamin Boucher

While modern large-scale datasets often consist of heterogeneous subpopulations -- for example, multiple demographic groups or multiple text corpora -- the standard practice of minimizing average loss fails to guarantee uniformly low losses…

Machine Learning · Computer Science 2022-08-12 John Duchi , Tatsunori Hashimoto , Hongseok Namkoong

In binary classification problems, mainly two approaches have been proposed; one is loss function approach and the other is uncertainty set approach. The loss function approach is applied to major learning algorithms such as support vector…

Machine Learning · Statistics 2012-05-01 Takafumi Kanamori , Akiko Takeda , Taiji Suzuki

Submodular set-functions have many applications in combinatorial optimization, as they can be minimized and approximately maximized in polynomial time. A key element in many of the algorithms and analyses is the possibility of extending the…

Machine Learning · Computer Science 2016-02-24 Francis Bach

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 address the problem of aggregating an ensemble of predictors with known loss bounds in a semi-supervised binary classification setting, to minimize prediction loss incurred on the unlabeled data. We find the minimax optimal predictions…

Machine Learning · Computer Science 2016-11-08 Akshay Balsubramani , Yoav Freund

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

Learning high-dimensional distributions is often done with explicit likelihood modeling or implicit modeling via minimizing integral probability metrics (IPMs). In this paper, we expand this learning paradigm to stochastic orders, namely,…

Machine Learning · Statistics 2022-11-11 Carles Domingo-Enrich , Yair Schiff , Youssef Mroueh

Regularized empirical risk minimization with constrained labels (in contrast to fixed labels) is a remarkably general abstraction of learning. For common loss and regularization functions, this optimization problem assumes the form of a…

Machine Learning · Computer Science 2016-02-23 Iaroslav Shcherbatyi , Bjoern Andres

This work proposes a new loss function targeting classification problems, utilizing a source of information overlooked by cross entropy loss. First, we derive a series of the tightest upper and lower bounds for the probability of a random…

Computer Vision and Pattern Recognition · Computer Science 2021-10-26 Ali Ghobadzadeh , Amir Lashkari

In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it…

Machine Learning · Computer Science 2015-05-08 Bharath Sankaran , Marjan Ghazvininejad , Xinran He , David Kale , Liron Cohen

Learning with a {\it convex loss} function has been a dominating paradigm for many years. It remains an interesting question how non-convex loss functions help improve the generalization of learning with broad applicability. In this paper,…

Machine Learning · Computer Science 2018-05-22 Yi Xu , Shenghuo Zhu , Sen Yang , Chi Zhang , Rong Jin , Tianbao Yang

In this paper we extend the setting of the online prediction with expert advice to function-valued forecasts. At each step of the online game several experts predict a function, and the learner has to efficiently aggregate these functional…

Machine Learning · Computer Science 2025-01-07 Alexander Korotin , Vladimir V'yugin , Evgeny Burnaev

We study unconstrained optimization problems with nonsmooth and convex objective function in the form of a mathematical expectation. The proposed method approximates the expected objective function with a sample average function using…

Optimization and Control · Mathematics 2022-11-03 Natasa Krejic , Natasa Krklec Jerinkic , Tijana Ostojic

We propose an extended generalization of the pseudo Huber loss formulation. We show that using the log-exp transform together with the logistic function, we can create a loss which combines the desirable properties of the strictly convex…

Machine Learning · Statistics 2022-02-24 Kaan Gokcesu , Hakan Gokcesu

We consider stochastic optimization problems involving an expected value of a nonlinear function of a base random vector and a conditional expectation of another function depending on the base random vector, a dependent random vector, and…

Optimization and Control · Mathematics 2024-05-20 Andrzej Ruszczyński , Shangzhe Yang

We consider the problem of optimising the expected value of a loss functional over a nonlinear model class of functions, assuming that we have only access to realisations of the gradient of the loss. This is a classical task in statistics,…

Optimization and Control · Mathematics 2026-02-02 Robert Gruhlke , Anthony Nouy , Philipp Trunschke

We demonstrate equivalence between the reinforcement learning problem and the supervised classification problem. We consequently equate the exploration exploitation trade-off in reinforcement learning to the dataset imbalance problem in…

Machine Learning · Computer Science 2023-08-09 Hasham Burhani , Xiao Qi Shi , Jonathan Jaegerman , Daniel Balicki

In the context of linear regression, we construct a data-driven convex loss function with respect to which empirical risk minimisation yields optimal asymptotic variance in the downstream estimation of the regression coefficients. At the…

Statistics Theory · Mathematics 2025-05-29 Oliver Y. Feng , Yu-Chun Kao , Min Xu , Richard J. Samworth