Learning to Defer to Multiple Experts: Consistent Surrogate Losses, Confidence Calibration, and Conformal Ensembles

• URL: http://arxiv.org/abs/2210.16955v1
• Date: Sun, 30 Oct 2022 21:27:29 GMT
• Title: Learning to Defer to Multiple Experts: Consistent Surrogate Losses, Confidence Calibration, and Conformal Ensembles
• Authors: Rajeev Verma, Daniel Barrej\'on, Eric Nalisnick
• Abstract summary: We study the statistical properties of learning to defer (L2D) to multiple experts. We address the open problems of deriving a consistent surrogate loss, confidence calibration, and principled ensembling of experts.
• Score: 0.966840768820136
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the statistical properties of learning to defer (L2D) to multiple experts. In particular, we address the open problems of deriving a consistent surrogate loss, confidence calibration, and principled ensembling of experts. Firstly, we derive two consistent surrogates -- one based on a softmax parameterization, the other on a one-vs-all (OvA) parameterization -- that are analogous to the single expert losses proposed by Mozannar and Sontag (2020) and Verma and Nalisnick (2022), respectively. We then study the frameworks' ability to estimate P( m_j = y | x ), the probability that the jth expert will correctly predict the label for x. Theory shows the softmax-based loss causes mis-calibration to propagate between the estimates while the OvA-based loss does not (though in practice, we find there are trade offs). Lastly, we propose a conformal inference technique that chooses a subset of experts to query when the system defers. We perform empirical validation on tasks for galaxy, skin lesion, and hate speech classification.

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