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We study the statistical properties of learning to defer (L2D) to multiple experts. In particular, we address the open problems of deriving a consistent surrogate loss, confidence calibration, and principled ensembling of experts. Firstly,…

Machine Learning · Statistics 2023-02-24 Rajeev Verma , Daniel Barrejón , Eric Nalisnick

Learning algorithms are often used in conjunction with expert decision makers in practical scenarios, however this fact is largely ignored when designing these algorithms. In this paper we explore how to learn predictors that can either…

Machine Learning · Computer Science 2021-01-26 Hussein Mozannar , David Sontag

We present a study of surrogate losses and algorithms for the general problem of learning to defer with multiple experts. We first introduce a new family of surrogate losses specifically tailored for the multiple-expert setting, where the…

Machine Learning · Computer Science 2024-04-02 Anqi Mao , Mehryar Mohri , Yutao Zhong

The problem of learning to defer with multiple experts consists of optimally assigning input instances to experts, balancing the trade-off between their accuracy and computational cost. This is a critical challenge in natural language…

Machine Learning · Computer Science 2025-12-30 Anqi Mao , Mehryar Mohri , Yutao Zhong

Learning algorithms can be significantly improved by routing complex or uncertain inputs to specialized experts, balancing accuracy with computational cost. This approach, known as learning to defer, is essential in domains like natural…

Machine Learning · Computer Science 2026-05-01 Corinna Cortes , Anqi Mao , Mehryar Mohri , Yutao Zhong

The learning to defer (L2D) framework has the potential to make AI systems safer. For a given input, the system can defer the decision to a human if the human is more likely than the model to take the correct action. We study the…

Machine Learning · Computer Science 2022-06-22 Rajeev Verma , Eric Nalisnick

The Softmax loss is one of the most widely employed surrogate objectives for classification and ranking tasks. To elucidate its theoretical properties, the Fenchel-Young framework situates it as a canonical instance within a broad family of…

Machine Learning · Computer Science 2026-02-02 Yuanhao Pu , Defu Lian , Enhong Chen

Machine learning models are often implemented in cohort with humans in the pipeline, with the model having an option to defer to a domain expert in cases where it has low confidence in its inference. Our goal is to design mechanisms for…

Machine Learning · Computer Science 2021-12-14 Vijay Keswani , Matthew Lease , Krishnaram Kenthapadi

Learning to defer uncertain predictions to costly experts offers a powerful strategy for improving the accuracy and efficiency of machine learning systems. However, standard training procedures for deferral algorithms typically require…

Machine Learning · Computer Science 2025-10-31 Giulia DeSalvo , Clara Mohri , Mehryar Mohri , Yutao Zhong

Learning-to-Defer routes each input to the expert that minimizes expected cost, but it assumes that the information available to every expert is fixed at decision time. Many modern systems violate this assumption: after selecting an expert,…

Machine Learning · Statistics 2026-05-29 Yannis Montreuil , Leïna Montreuil , Axel Carlier , Lai Xing Ng , Wei Tsang Ooi

With model trustworthiness being crucial for sensitive real-world applications, practitioners are putting more and more focus on improving the uncertainty calibration of deep neural networks. Calibration errors are designed to quantify the…

Machine Learning · Computer Science 2024-03-14 Sebastian G. Gruber , Florian Buettner

When facing uncertainty, decision-makers want predictions they can trust. A machine learning provider can convey confidence to decision-makers by guaranteeing their predictions are distribution calibrated -- amongst the inputs that receive…

Machine Learning · Statistics 2021-07-14 Shengjia Zhao , Michael P. Kim , Roshni Sahoo , Tengyu Ma , Stefano Ermon

Learning to defer with multiple experts is a framework where the learner can choose to defer the prediction to several experts. While this problem has received significant attention in classification contexts, it presents unique challenges…

Machine Learning · Computer Science 2024-03-29 Anqi Mao , Mehryar Mohri , Yutao Zhong

Calibration of neural networks is a topical problem that is becoming more and more important as neural networks increasingly underpin real-world applications. The problem is especially noticeable when using modern neural networks, for which…

Machine Learning · Computer Science 2023-08-29 Ondrej Bohdal , Yongxin Yang , Timothy Hospedales

We study consistency properties of machine learning methods based on minimizing convex surrogates. We extend the recent framework of Osokin et al. (2017) for the quantitative analysis of consistency properties to the case of inconsistent…

Machine Learning · Computer Science 2019-01-10 Kirill Struminsky , Simon Lacoste-Julien , Anton Osokin

One of the goals of learning algorithms is to complement and reduce the burden on human decision makers. The expert deferral setting wherein an algorithm can either predict on its own or defer the decision to a downstream expert helps…

Machine Learning · Computer Science 2022-07-21 Mohammad-Amin Charusaie , Hussein Mozannar , David Sontag , Samira Samadi

A learning-to-defer (L2D) system decides, for each input, whether to predict on its own or to hand it to one of several available experts. The very well established recipe trains classifier and router jointly by treating the $K$ classes and…

Machine Learning · Statistics 2026-05-29 Yannis Montreuil , Axel Carlier , Lai Xing Ng , Wei Tsang Ooi

Decentralized sparsity learning has attracted a significant amount of attention recently due to its rapidly growing applications. To obtain the robust and sparse estimators, a natural idea is to adopt the non-smooth median loss combined…

Machine Learning · Statistics 2022-03-02 Weidong Liu , Xiaojun Mao , Xin Zhang

In this paper we refine the process of computing calibration functions for a number of multiclass classification surrogate losses. Calibration functions are a powerful tool for easily converting bounds for the surrogate risk (which can be…

Machine Learning · Statistics 2016-09-22 Bernardo Ávila Pires , Csaba Szepesvári

Normalization is a vital process for any machine learning task as it controls the properties of data and affects model performance at large. The impact of particular forms of normalization, however, has so far been investigated in limited…

Machine Learning · Computer Science 2022-06-22 Chintan Trivedi , Konstantinos Makantasis , Antonios Liapis , Georgios N. Yannakakis
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