No-gap stochastic luckiness regime

Characterize the constant-in-time regret behavior in the no-gap regime, where experts’ mean losses accumulate at the minimal mean without a strict off-face gap or a finite low-noise constant for a minimal-mean comparator.

Background

The paper proves constant-in-horizon expected regret under a low-noise condition and extends the result from point-mass comparators to diffuse comparators when there is a strict gap between the minimal-mean face and the remaining experts. The authors state that the unresolved case is the no-gap regime, including continua of experts or mean losses accumulating at the minimum, where that strict-gap argument does not apply.