Conversation-calibrated agents, efficiently constructible from any ML model, reach approximate agreement in few rounds while improving accuracy, generalizing Aumann-Aaronson theorems to d dimensions and action feedback.
An Elementary Predictor Obtaining $2\sqrt{T}+1$ Distance to Calibration
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abstract
Blasiok et al. [2023] proposed distance to calibration as a natural measure of calibration error that unlike expected calibration error (ECE) is continuous. Recently, Qiao and Zheng [2024] gave a non-constructive argument establishing the existence of an online predictor that can obtain $O(\sqrt{T})$ distance to calibration in the adversarial setting, which is known to be impossible for ECE. They leave as an open problem finding an explicit, efficient algorithm. We resolve this problem and give an extremely simple, efficient, deterministic algorithm that obtains distance to calibration error at most $2\sqrt{T}+1$.
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Tractable Agreement Protocols
Conversation-calibrated agents, efficiently constructible from any ML model, reach approximate agreement in few rounds while improving accuracy, generalizing Aumann-Aaronson theorems to d dimensions and action feedback.