The Optimal Sample Complexity of Pointwise Replicable Agnostic Learning
Pointwise replicability asks that two independently trained predictors, using the same random seed, agree at each fixed query with high probability. We determine its optimal agnostic sample complexity on finite and countable domains. For every nonempty binary class of finite VC dimension $d\ge1$, the required number of independent examples is $Θ\!\left(\frac{d}{ρ^2α^2}+\frac{\log(1/β)}{α^2}\right)$, uniformly over independent accuracy, failure, and disagreement parameters $α,β,ρ\in(0,1/10)$. The learner returns one binary function, may be improper, and uses unrestricted shared randomness. Its sample budget is fixed before observing data, and the replicability guarantee includes queries of...
| Authors | Guangjian Zhang |
|---|---|
| Primary category | cs.LG |
| Published | 18 October 2026 |
| Last updated at source | 18 October 2026 |
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