New stability framework handles heavy-tailed losses without boundedness

A team of researchers led by Qianqian Lei at the University of Chicago has released a paper (arXiv:2606.06855) that significantly relaxes the assumptions needed for algorithmic stability to guarantee generalization. Traditional high-probability generalization bounds rely on uniform boundedness or sub-Gaussian/sub-Weibull tails, which fail in many modern machine learning settings where losses can be heavy-tailed (e.g., in reinforcement learning or robust optimization).

The authors introduce concentration inequalities for functions of independent random variables under only a finite L_p moment condition—essentially requiring that the p-th moment of the loss exists. This extends McDiarmid's classic bounded-differences inequality to unbounded regimes. Using these tools, they derive sharp generalization bounds for empirical risk minimization, transductive regression, and meta-learning. The key insight: L_p stability (where the stability measure is bounded in L_p norm) is sufficient for good generalization even when individual losses are unbounded. This makes the theory applicable to a much wider range of practical algorithms and datasets.