Adaptive sampling under distributional drift

We consider the problem of maintaining calibrated estimates when the sampling distribution shifts faster than the evaluation window. The central claim is that a fixed-window estimator is not merely suboptimal but systematically biased in the direction of the most recent regime.

Section 3 develops the bound. Section 4 evaluates it on three public traces, two of which contain a documented regime change.

3. The bound

Let the drift rate be bounded above by δ per unit interval. We show that any estimator with a window of length w incurs excess error proportional to δw regardless of sample size, which is the result that motivates the adaptive scheme.