The Sharp Tail of Uniform Stability

Uniform stability controls how much one training example can change the loss at any test point. A new logarithmic-free upper bound shows that a $γ$-uniformly stable algorithm with loss in $[0,L]$ has generalization gap at most $O \left(γ\log(1/δ) +L\sqrt{\frac{\log(1/δ)}{n}}\right)$ with probability