Stability beyond Bounded Differences: Sharp Generalization Bounds under Finite $L_p$ Moments
While algorithmic stability is a central tool for understanding generalization of learning algorithms, existing high-probability guarantees typically rely on uniform boundedness or sub-Gaussian/sub-Weibull tail assumptions, which can be overly restrictive for modern settings with heavy-tailed or unbounded losses. We develop a stability-based framework that requires only a finite $L_p$ moment condition. Our first contribution is sharp concentration inequalities for functions of independent random variables under $L_p$ constraints, extending McDiarmid's bounded-differences techniques beyond the classical regime. Leveraging these results, we derive sharp high-probability generalization bound...
| Authors | Qianqian Lei, Soham Bonnerjee, Yuefeng Han et al. |
|---|---|
| Primary category | stat.ML |
| Published | 5 June 2026 |
| Last updated at source | 5 June 2026 |
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