Can smooth calibration achieve faster rates than traditional calibration?

Ascertain whether smooth calibration can be guaranteed at rates faster than those known for traditional calibration in adversarial online environments, and, if so, develop algorithms that achieve such improved rates.

Background

Smooth calibration relaxes standard calibration and supports guarantees for agents who smoothly best respond, with additional desirable properties such as deterministic procedures in adversarial settings. Despite these benefits, current results do not establish improved convergence rates over traditional calibration.

The authors explicitly state that it is not known whether smooth calibration can be obtained at faster rates, underscoring an open direction for improving learning dynamics under smooth response assumptions.