Theory and Algorithms for Learning with Multi-Class Abstention and Multi-Expert Deferral

• URL: http://arxiv.org/abs/2512.22886v1
• Date: Sun, 28 Dec 2025 11:33:39 GMT
• Title: Theory and Algorithms for Learning with Multi-Class Abstention and Multi-Expert Deferral
• Authors: Anqi Mao,
• Abstract summary: Large language models (LLMs) have achieved remarkable performance but face critical challenges: hallucinations and high inference costs.<n>Leveraging multiple experts offers a solution: deferring uncertain inputs to more capable experts improves reliability.<n>This thesis presents a comprehensive study of this problem and the related problem of learning with abstention, supported by strong consistency guarantees.
• Score: 20.76255397215973
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Large language models (LLMs) have achieved remarkable performance but face critical challenges: hallucinations and high inference costs. Leveraging multiple experts offers a solution: deferring uncertain inputs to more capable experts improves reliability, while routing simpler queries to smaller, distilled models enhances efficiency. This motivates the problem of learning with multiple-expert deferral. This thesis presents a comprehensive study of this problem and the related problem of learning with abstention, supported by strong consistency guarantees. First, for learning with abstention (a special case of deferral), we analyze score-based and predictor-rejector formulations in multi-class classification. We introduce new families of surrogate losses and prove strong non-asymptotic, hypothesis set-specific consistency guarantees, resolving two existing open questions. We analyze both single-stage and practical two-stage settings, with experiments on CIFAR-10, CIFAR-100, and SVHN demonstrating the superior performance of our algorithms. Second, we address general multi-expert deferral in classification. We design new surrogate losses for both single-stage and two-stage scenarios and prove they benefit from strong $H$-consistency bounds. For the two-stage scenario, we show that our surrogate losses are realizable $H$-consistent for constant cost functions, leading to effective new algorithms. Finally, we introduce a novel framework for regression with deferral to address continuous label spaces. Our versatile framework accommodates multiple experts and various cost structures, supporting both single-stage and two-stage methods. It subsumes recent work on regression with abstention. We propose new surrogate losses with proven $H$-consistency and demonstrate the empirical effectiveness of the resulting algorithms.

Related papers

• Is Softmax Loss All You Need? A Principled Analysis of Softmax-family Loss [91.61796429377041]
  The Softmax loss is one of the most widely employed surrogate objectives for classification and ranking tasks.<n>We investigate whether different surrogates achieve consistency with classification and ranking metrics, and analyze their gradient dynamics to reveal distinct convergence behaviors.<n>Our results establish a principled foundation and offer practical guidance for loss selections in large-class machine learning applications.
  arXiv  Detail & Related papers  (2026-01-30T09:24:52Z)
• Beyond Redundancy: Diverse and Specialized Multi-Expert Sparse Autoencoder [59.89996751196727]
  Sparse autoencoders (SAEs) have emerged as a powerful tool for interpreting large language models.<n>SAEs' hidden layers have high dimensionality to satisfy sparsity constraints, resulting in prohibitive training and inference costs.<n>Recent Mixture of Experts (MoE) approaches attempt to address this by SAEs into narrower expert networks with gated activation.<n>We propose two key innovations: (1) Multiple Expert Activation that simultaneously engages semantically weighted expert subsets to encourage specialization, and (2) Feature Scaling that enhances diversity through adaptive high-frequency scaling.
  arXiv  Detail & Related papers  (2025-11-07T22:19:34Z)
• Mastering Multiple-Expert Routing: Realizable $H$-Consistency and Strong Guarantees for Learning to Defer [30.389055604165222]
  This paper introduces novel surrogate loss functions and efficient algorithms with strong theoretical learning guarantees.<n>We address open questions regarding realizable $H$-consistency, $H$-consistency bounds, and Bayes-consistency for both single-stage and two-stage learning scenarios.<n>We derive new surrogate losses that achieve realizable $H$-consistency, $H$-consistency bounds, and Bayes-consistency for the two-expert scenario and, under natural assumptions, multiple-expert scenario.
  arXiv  Detail & Related papers  (2025-06-25T17:48:58Z)
• Unlocking the Potential of Difficulty Prior in RL-based Multimodal Reasoning [69.64809103333839]
  We investigate how explicitly modeling problem's difficulty prior information shapes the effectiveness of reinforcement learning based fine-tuning for multimodal reasoning.<n>Our approach demonstrates significant performances across various multi-modal mathematical reasoning benchmarks with only 2K+0.6K two-stage training data.
  arXiv  Detail & Related papers  (2025-05-19T15:43:10Z)
• Why Do Multi-Agent LLM Systems Fail? [87.90075668488434]
  We introduce MAST-Data, a comprehensive dataset of 1600+ annotated traces collected across 7 popular MAS frameworks.<n>We build the first Multi-Agent System Failure taxonomy (MAST)<n>We leverage MAST and MAST-Data to analyze failure patterns across models (GPT4, Claude 3, Qwen2.5, CodeLlama) and tasks (coding, math, general agent)
  arXiv  Detail & Related papers  (2025-03-17T19:04:38Z)
• A Two-Stage Learning-to-Defer Approach for Multi-Task Learning [3.4289478404209826]
  We introduce a novel Two-Stage L2D framework for multi-task learning that integrates classification and regression through a unified deferral mechanism.<n>Our method leverages a two-stage surrogate loss family, which we prove to be both Bayes-consistent and $(mathcalG, mathcalR)$-consistent.
  arXiv  Detail & Related papers  (2024-10-21T07:44:57Z)
• Regression with Multi-Expert Deferral [30.389055604165222]
  Learning to defer with multiple experts is a framework where the learner can choose to defer the prediction to several experts. We present a novel framework of regression with deferral, which involves deferring the prediction to multiple experts. We introduce new surrogate loss functions for both scenarios and prove that they are supported by $H$-consistency bounds.
  arXiv  Detail & Related papers  (2024-03-28T15:26:38Z)
• Principled Approaches for Learning to Defer with Multiple Experts [30.389055604165222]
  We introduce a new family of surrogate losses specifically tailored for the multiple-expert setting. We prove that these surrogate losses benefit from strong $H$-consistency bounds.
  arXiv  Detail & Related papers  (2023-10-23T10:19:09Z)
• Predictor-Rejector Multi-Class Abstention: Theoretical Analysis and Algorithms [30.389055604165222]
  We study the key framework of learning with abstention in the multi-class classification setting. In this setting, the learner can choose to abstain from making a prediction with some pre-defined cost. We introduce several new families of surrogate losses for which we prove strong non-asymptotic and hypothesis set-specific consistency guarantees.
  arXiv  Detail & Related papers  (2023-10-23T10:16:27Z)
• A Unifying Perspective on Multi-Calibration: Game Dynamics for Multi-Objective Learning [63.20009081099896]
  We provide a unifying framework for the design and analysis of multicalibrated predictors. We exploit connections to game dynamics to achieve state-of-the-art guarantees for a diverse set of multicalibration learning problems.
  arXiv  Detail & Related papers  (2023-02-21T18:24:17Z)
• Adversarial Robustness with Semi-Infinite Constrained Learning [177.42714838799924]
  Deep learning to inputs perturbations has raised serious questions about its use in safety-critical domains. We propose a hybrid Langevin Monte Carlo training approach to mitigate this issue. We show that our approach can mitigate the trade-off between state-of-the-art performance and robust robustness.
  arXiv  Detail & Related papers  (2021-10-29T13:30:42Z)
• Softmax with Regularization: Better Value Estimation in Multi-Agent Reinforcement Learning [72.28520951105207]
  Overestimation in $Q$-learning is an important problem that has been extensively studied in single-agent reinforcement learning. We propose a novel regularization-based update scheme that penalizes large joint action-values deviating from a baseline. We show that our method provides a consistent performance improvement on a set of challenging StarCraft II micromanagement tasks.
  arXiv  Detail & Related papers  (2021-03-22T14:18:39Z)
• Reparameterized Variational Divergence Minimization for Stable Imitation [57.06909373038396]
  We study the extent to which variations in the choice of probabilistic divergence may yield more performant ILO algorithms. We contribute a re parameterization trick for adversarial imitation learning to alleviate the challenges of the promising $f$-divergence minimization framework. Empirically, we demonstrate that our design choices allow for ILO algorithms that outperform baseline approaches and more closely match expert performance in low-dimensional continuous-control tasks.
  arXiv  Detail & Related papers  (2020-06-18T19:04:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.