Logarithmic-Free Moment and Generalization Bounds for Uniformly Stable Algorithms
Uniform stability is a classical tool for controlling the generalization error of a learning algorithm. Bousquet, Klochkov, and Zhivotovskiy (2020) showed that the problem can be reduced to a moment inequality for a sum of weakly interacting functions of independent random variables. Their bound contains an additional factor $\log n$, and they asked whether this factor can be removed. We answer this upper-bound question affirmatively. More specifically, let $Z=(Z_1,\ldots,Z_n)$ have independent coordinates and let $g_i(Z)$ satisfy $\mathbb E[g_i(Z)\mid Z_{-i}]=0, \ \left| \mathbb E[g_i(Z)\mid Z_i]\right|\le M, \ \text{for every } i = 1, \dots, n, $ where $Z_{-i}$ denotes all coordinates e...
| Authors | Thanh Nguyen-Cung, Binh T. Nguyen |
|---|---|
| Primary category | stat.ML |
| Published | 10 August 2026 |
| Last updated at source | 1 September 2026 |
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