Related papers: Smooth Calibration, Leaky Forecasts, Finite Recall, and Nash Dynamics

Smooth Calibration, Leaky Forecasts, Finite Recall, and Nash Dynamics

URL: http://arxiv.org/abs/2210.07152v1
Date: Thu, 13 Oct 2022 16:34:55 GMT
Title: Smooth Calibration, Leaky Forecasts, Finite Recall, and Nash Dynamics
Authors: Dean P. Foster and Sergiu Hart
Abstract summary: We propose to smooth out the calibration score, which measures how good a forecaster is, by combining nearby forecasts. We show that smooth calibration can be guaranteed by deterministic procedures.
Score: 8.858351266850544
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We propose to smooth out the calibration score, which measures how good a forecaster is, by combining nearby forecasts. While regular calibration can be guaranteed only by randomized forecasting procedures, we show that smooth calibration can be guaranteed by deterministic procedures. As a consequence, it does not matter if the forecasts are leaked, i.e., made known in advance: smooth calibration can nevertheless be guaranteed (while regular calibration cannot). Moreover, our procedure has finite recall, is stationary, and all forecasts lie on a finite grid. To construct the procedure, we deal also with the related setups of online linear regression and weak calibration. Finally, we show that smooth calibration yields uncoupled finite-memory dynamics in n-person games "smooth calibrated learning" in which the players play approximate Nash equilibria in almost all periods (by contrast, calibrated learning, which uses regular calibration, yields only that the time-averages of play are approximate correlated equilibria).

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