Realizable $H$-Consistent and Bayes-Consistent Loss Functions for Learning to Defer
<|reference_start|>Realizable $H$-Consistent and Bayes-Consistent Loss Functions for Learning to Defer: We present a comprehensive study of surrogate loss functions for learning to defer. We introduce a broad family of surrogate losses, parameterized by a non-increasing function $\Psi$, and establish their realizable $H$-consistency under mild conditions. For cost functions based on classification error, we further show that these losses admit $H$-consistency bounds when the hypothesis set is symmetric and complete, a property satisfied by common neural network and linear function hypothesis sets. Our results also resolve an open question raised in previous work (Mozannar et al., 2023) by proving the realizable $H$-consistency and Bayes-consistency of a specific surrogate loss. Furthermore, we identify choices of $\Psi$ that lead to $H$-consistent surrogate losses for any general cost function, thus achieving Bayes-consistency, realizable $H$-consistency, and $H$-consistency bounds simultaneously. We also investigate the relationship between $H$-consistency bounds and realizable $H$-consistency in learning to defer, highlighting key differences from standard classification. Finally, we empirically evaluate our proposed surrogate losses and compare them with existing baselines.<|reference_end|>
@article{mao2024realizable,
    title={Realizable $H$-Consistent and Bayes-Consistent Loss Functions for
  Learning to Defer},
    author={Anqi Mao, Mehryar Mohri, Yutao Zhong},
    journal={arXiv preprint arXiv:2407.13732},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.13732},
    primaryClass={cs.LG stat.ML}
}