Intermediate Group Family Sizes for Multicalibration
Do minimax multicalibration rates exhibit sharp thresholds or smooth interpolation as |G| grows?
6
Scaling Regimes
Smooth
Interpolation Type
1.5-2x
Polylog Separation
No
Sharp Threshold
Key Findings
Multicalibration rates interpolate smoothly between constant and linear regimes
No sharp threshold detected at any group family size
Polylog regime (|G| = log^2 T) shows moderate 1.5-2x separation from marginal calibration
Rate exponent decreases smoothly, consistent with continuous dependence on |G|/T
Rate Landscape
Threshold Detection
Scaling Exponents
Smoothness (Second Differences)