{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/learning-to-defer-to-multiple-experts","title":"Learning to Defer to Multiple Experts: Consistent Surrogate Losses, Confidence Calibration, and Conformal Ensembles","arxiv_id":"2210.16955","date":"2022-10-30","proceeding":null,"authors":["Rajeev Verma","Daniel Barrejón","Eric Nalisnick"],"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.","url_abs":"https://arxiv.org/abs/2210.16955v2","url_pdf":"https://arxiv.org/pdf/2210.16955v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"learning-to-defer-to-multiple-experts","repo_url":"https://github.com/rajevv/multi_l2d","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"softmax","method_name":"Softmax"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2210.16955","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}