Beyond Augmented-Action Surrogates for Multi-Expert Learning-to-Defer

• URL: http://arxiv.org/abs/2604.09414v2
• Date: Fri, 17 Apr 2026 07:35:05 GMT
• Title: Beyond Augmented-Action Surrogates for Multi-Expert Learning-to-Defer
• Abstract summary: Multi-expert learning-to-defer surrogates are statistically consistent, yet they can underfit, suppress useful experts, or degrade as the expert pool grows.<n>We trace these failures to a shared architectural choice: casting classes and experts as actions inside one augmented prediction geometry.<n>We introduce a decoupled surrogate that estimates the class posterior with a softmax and each expert utility with an independent sigmoid.
• Score: 6.792743621449621
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Existing multi-expert learning-to-defer surrogates are statistically consistent, yet they can underfit, suppress useful experts, or degrade as the expert pool grows. We trace these failures to a shared architectural choice: casting classes and experts as actions inside one augmented prediction geometry. Consistency governs the population target; it says nothing about how the surrogate distributes gradient mass during training. We analyze five surrogates along both axes and show that each trades a fix on one for a failure on the other. We then introduce a decoupled surrogate that estimates the class posterior with a softmax and each expert utility with an independent sigmoid. It admits an $\mathcal{H}$-consistency bound whose constant is $J$-independent for fixed per-expert weight $β{=}λ/J$, and its gradients are free of the amplification, starvation, and coupling pathologies of the augmented family. Experiments on synthetic benchmarks, CIFAR-10, CIFAR-10H, and Covertype confirm that the decoupled surrogate is the only method that avoids amplification under redundancy, preserves rare specialists, and consistently improves over a standalone classifier across all settings.

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