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Forecast-Hedging and Calibration

Author

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  • Sergiu Hart
  • Dean P. Foster
Abstract
Calibration means that for each forecast x the average of the realized actions in the periods in which the forecast was x is, in the long run, close to x. Calibration can always be guaranteed (Foster and Vohra 1998), but it requires the forecasting procedure to be stochastic. By contrast, smooth calibration, which combines in a continuous manner nearby forecasts, can be guaranteed by a deterministic procedure (Foster and Hart 2018). In the present paper we develop the concept of forecast-hedging, which consists of choosing the forecasts in such a way that, no matter what the realized action will be, the expected forecasting track record can only improve. This approach integrates the existing calibration results by obtaining them all from the same simple basic argument, and at the same time differentiates between them according to the forecast-hedging tools that are used: deterministic and fixed point-based vs. stochastic and minimax-based. Additional benefits are new calibration procedures in the one-dimensional case that are simpler than all known such procedures, and a short proof for deterministic smooth calibration, in contrast to the complicated existing proof.

Suggested Citation

  • Sergiu Hart & Dean P. Foster, 2019. "Forecast-Hedging and Calibration," Discussion Paper Series dp731, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp731
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    File URL: http://www.ma.huji.ac.il/hart/abs/calib-int.html
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    References listed on IDEAS

    as
    1. Foster, Dean P. & Hart, Sergiu, 2018. "Smooth calibration, leaky forecasts, finite recall, and Nash dynamics," Games and Economic Behavior, Elsevier, vol. 109(C), pages 271-293.
    2. Foster, Dean P., 1999. "A Proof of Calibration via Blackwell's Approachability Theorem," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 73-78, October.
    3. Foster, Dean P. & Vohra, Rakesh, 1999. "Regret in the On-Line Decision Problem," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 7-35, October.
    4. Sergiu Hart & Andreu Mas-Colell, 2013. "Stochastic Uncoupled Dynamics And Nash Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 8, pages 165-189, World Scientific Publishing Co. Pte. Ltd..
    5. Fudenberg, Drew & Levine, David K., 1999. "An Easier Way to Calibrate," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 131-137, October.
    6. Sergiu Hart & Andreu Mas-Colell, 2013. "Uncoupled Dynamics Do Not Lead To Nash Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 7, pages 153-163, World Scientific Publishing Co. Pte. Ltd..
    7. Sergiu Hart, 2013. "Nash Equilibrium And Dynamics," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 12, pages 289-293, World Scientific Publishing Co. Pte. Ltd..
    8. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October.
    9. Eddie Dekel & Yossi Feinberg, 2006. "Non-Bayesian Testing of a Stochastic Prediction," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 893-906.
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    Cited by:

    1. Foster, Dean & Hart, Sergiu, 2023. ""Calibeating": beating forecasters at their own game," Theoretical Economics, Econometric Society, vol. 18(4), November.
    2. Sergiu Hart, 2022. "Calibrated Forecasts: The Minimax Proof," Papers 2209.05863, arXiv.org, revised Feb 2023.
    3. Atulya Jain & Vianney Perchet, 2024. "Calibrated Forecasting and Persuasion," Papers 2406.15680, arXiv.org.
    4. Varun Gupta & Christopher Jung & Georgy Noarov & Mallesh M. Pai & Aaron Roth, 2021. "Online Multivalid Learning: Means, Moments, and Prediction Intervals," Papers 2101.01739, arXiv.org.

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