Realizable $H$-Consistent and Bayes-Consistent Loss Functions for Learning to Defer
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| Format: | Preprint |
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2024
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| _version_ | 1866911960905285632 |
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| author | Mao, Anqi Mohri, Mehryar Zhong, Yutao |
| author_facet | Mao, Anqi Mohri, Mehryar Zhong, Yutao |
| contents | 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 $Ψ$, 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 $Ψ$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_13732 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Realizable $H$-Consistent and Bayes-Consistent Loss Functions for Learning to Defer Mao, Anqi Mohri, Mehryar Zhong, Yutao Machine Learning 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 $Ψ$, 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 $Ψ$ 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. |
| title | Realizable $H$-Consistent and Bayes-Consistent Loss Functions for Learning to Defer |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2407.13732 |