Hi, @bgoyal.
As explained in this lecture, computing the exponentially weighted average is approximately equivalent to taking the average of the last 1/(1 - Beta) days.
As you can see, 1/(1 - Beta) is very sensitive to small changes in Beta when Beta is close to 1:
If you sample uniformly, more often than not you’ll end up exploring a small subset of the range of 1/(1 - Beta):
Instead, you want to sample more densely (the formulas were removed, but I hope the point is clear) in the regions where Beta is closer to 1:
Let me know if that helped 