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Loss Minimization Yields Multicalibration for Large Neural Networks

Authors Jarosław Błasiok, Parikshit Gopalan, Lunjia Hu, Adam Tauman Kalai, Preetum Nakkiran

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  • Theory of computation → Machine learning theory
  • Computing methodologies → Neural networks
Keywords
  • Multi-group fairness
  • loss minimization
  • neural networks

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Abstract

Multicalibration is a notion of fairness for predictors that requires them to provide calibrated predictions across a large set of protected groups. Multicalibration is known to be a distinct goal than loss minimization, even for simple predictors such as linear functions. 
In this work, we consider the setting where the protected groups can be represented by neural networks of size k, and the predictors are neural networks of size n > k. We show that minimizing the squared loss over all neural nets of size n implies multicalibration for all but a bounded number of unlucky values of n. We also give evidence that our bound on the number of unlucky values is tight, given our proof technique. Previously, results of the flavor that loss minimization yields multicalibration were known only for predictors that were near the ground truth, hence were rather limited in applicability. Unlike these, our results rely on the expressivity of neural nets and utilize the representation of the predictor.

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Jarosław Błasiok, Parikshit Gopalan, Lunjia Hu, Adam Tauman Kalai, and Preetum Nakkiran. Loss Minimization Yields Multicalibration for Large Neural Networks. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 17:1-17:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ITCS.2024.17

Author Details

Jarosław Błasiok
  • ETH Zürich, Switzerland
Parikshit Gopalan
  • Apple, Palo Alto, CA, USA
Lunjia Hu
  • Stanford University, CA, USA
Adam Tauman Kalai
  • Microsoft Research, Cambridge, MA, USA
Preetum Nakkiran
  • Apple, Palo Alto, CA, USA

Funding

  • Błasiok, Jarosław: JB is supported by a Junior Fellowship from the Simons Society of Fellows.
  • Hu, Lunjia: Part of this work was performed while LH was interning at Apple. LH is also supported by Moses Charikar’s and Omer Reingold’s Simons Investigators awards, Omer Reingold’s NSF Award IIS-1908774, and the Simons Foundation Collaboration on the Theory of Algorithmic Fairness.

Acknowledgements

We thank Ryan O'Donnell and Rocco Servedio for suggesting the current proof of Lemma 14. We also thank Barry-John Theobald for comments on an early draft.

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