The Sample Complexity of Distributionally Robust PAC Learning under Cressie--Read Divergences
We study distributionally robust PAC learning for the $0$--$1$-loss, where adversarial perturbations of the data distribution are constrained by a Cressie--Read divergence of order $k>1$ and radius $ρ\geq 0$. For hypothesis classes with VC dimension $d$, we establish realizable and agnostic sample-complexity bounds tight up to constant and logarithmic factors, respectively; ordinary empirical risk minimization attains both rates up to logarithmic factors. For target accuracy $\varepsilon\in(0,1)$ and confidence $δ\in(0,1)$, their respective orders are \[ \max\!\left\{\frac{1}{\varepsilon}, \frac{ρ^{\frac 1{k-1}}}{\varepsilon^{k_\star}} \right\}\cdot(d+\log δ^{-1}) \qquad\text{and}\qquad \...
| Authors | Elad Aigner-Horev, Daniel Rosenberg, Roi Weiss |
|---|---|
| Primary category | cs.LG |
| Published | 5 August 2026 |
| Last updated at source | 5 August 2026 |
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