# Consistent Learning-to-Defer with Expert-Conditional Advice

arXiv: https://arxiv.org/abs/2603.14324 · HTML: https://mlsanity.com/paper/2603.14324/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 57 references that are in the map.
- First posted on arXiv 15 Mar 2026.

## Builds on (most cited first, 30 of 35)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [REALM: Retrieval-Augmented Language Model Pre-Training](https://mlsanity.com/paper/2002.08909/) (2020)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [DeBERTaV3: Improving DeBERTa using ELECTRA-Style Pre-Training with Gradient-Disentangled Embedding Sharing](https://mlsanity.com/paper/2111.09543/) (2021)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Consistent Estimators for Learning to Defer to an Expert](https://mlsanity.com/paper/2006.01862/) (2020)
- [Predict Responsibly: Improving Fairness and Accuracy by Learning to Defer](https://mlsanity.com/paper/1711.06664/) (2017)
- [Towards Unbiased and Accurate Deferral to Multiple Experts](https://mlsanity.com/paper/2102.13004/) (2021)
- [Who Should Predict? Exact Algorithms For Learning to Defer to Humans](https://mlsanity.com/paper/2301.06197/) (2023)
- [Learning to Defer to Multiple Experts: Consistent Surrogate Losses, Confidence Calibration, and Conformal Ensembles](https://mlsanity.com/paper/2210.16955/) (2022)
- [Sample Efficient Learning of Predictors that Complement Humans](https://mlsanity.com/paper/2207.09584/) (2022)
- [On the Calibration of Multiclass Classification with Rejection](https://mlsanity.com/paper/1901.10655/) (2019)
- [Combining Human Predictions with Model Probabilities via Confusion Matrices and Calibration](https://mlsanity.com/paper/2109.14591/) (2021)
- [Forming Effective Human-AI Teams: Building Machine Learning Models that Complement the Capabilities of Multiple Experts](https://mlsanity.com/paper/2206.07948/) (2022)
- [Principled Approaches for Learning to Defer with Multiple Experts](https://mlsanity.com/paper/2310.14774/) (2023)
- [Predictor-Rejector Multi-Class Abstention: Theoretical Analysis and Algorithms](https://mlsanity.com/paper/2310.14772/) (2023)
- [Theoretically Grounded Loss Functions and Algorithms for Score-Based Multi-Class Abstention](https://mlsanity.com/paper/2310.14770/) (2023)
- [Regression with Multi-Expert Deferral](https://mlsanity.com/paper/2403.19494/) (2024)
- [Learning to Defer to a Population: A Meta-Learning Approach](https://mlsanity.com/paper/2403.02683/) (2024)
- [In Defense of Softmax Parametrization for Calibrated and Consistent Learning to Defer](https://mlsanity.com/paper/2311.01106/) (2023)
- [A Two-Stage Learning-to-Defer Approach for Multi-Task Learning](https://mlsanity.com/paper/2410.15729/) (2024)
- [Trustworthy and Practical AI for Healthcare: A Guided Deferral System with Large Language Models](https://mlsanity.com/paper/2406.07212/) (2024)
- [Adversarial Robustness in Two-Stage Learning-to-Defer: Algorithms and Guarantees](https://mlsanity.com/paper/2502.01027/) (2025)
- [Optimal Query Allocation in Extractive QA with LLMs: A Learning-to-Defer Framework with Theoretical Guarantees](https://mlsanity.com/paper/2410.15761/) (2024)
- [Counterfactual Inference of Second Opinions](https://mlsanity.com/paper/2203.08653/) (2022)
- [A Causal Framework for Evaluating Deferring Systems](https://mlsanity.com/paper/2405.18902/) (2024)
- [Learning-to-defer for sequential medical decision-making under uncertainty](https://mlsanity.com/paper/2109.06312/) (2021)
- [Improving Learning-to-Defer Algorithms Through Fine-Tuning](https://mlsanity.com/paper/2112.10768/) (2021)
- [Why Ask One When You Can Ask k? Learning-to-Defer to the Top-k Experts](https://mlsanity.com/paper/2504.12988/) (2025)

## Built on by (most cited first, 3 of 3)

- [Beyond Augmented-Action Surrogates for Multi-Expert Learning-to-Defer](https://mlsanity.com/paper/2604.09414/) (2026)
- [Mind the Gap: Structure-Aware Consistency in Preference Learning](https://mlsanity.com/paper/2604.27733/) (2026)
- [A Query Is Not a Commitment: Learning to Correct Expert Answers in Online Deferral](https://mlsanity.com/paper/2610.07084/) (2026)

## Abstract (arXiv)

We introduce learning-to-defer with advice, a new setting in which a system learns both which expert should handle an input and which information that expert should receive. The policy acts before observing advice and minimizes prediction loss plus expert and acquisition fees. Training may reveal all advice sources or only a subset on each record. We show that composing routing and advice losses can be inconsistent and that augmented training can incur avoidable estimation variance. We propose reference conditional classification, which jointly learns a fixed expert's error probability and each action's error conditional on that expert's success or failure. The reference outcome is observed on every labeled record, so records with missing advice still inform the estimates. We prove a consistency bound for bounded task losses, show that limited training preserves the full population objective, and establish variance reductions for the analyzed fits. On FEVER and Sensitive, full training has the lowest mean dev loss at every evaluated fee, while limited training improves on full training at most matched acquisition budgets.