The Optimal Sample Complexity of Pointwise Replicable Agnostic Learning

Key points

• Pointwise replicability asks that two independently trained predictors, using the same random seed, agree at each fixed query with high probability.1
• 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 $α,β,ρ\in(0,1/10)$.1
• The learner returns one binary function, may be improper, and uses unrestricted shared randomness.1
• The main construction combines an ensemble of empirical-risk minimizers with a smooth, signal-dependent risk decomposition.1

Sources (1)

• [1]The Optimal Sample Complexity of Pointwise Replicable Agnostic Learning
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 18, 07:08 AM

  We determine its optimal agnostic sample complexity on finite and countable domains.

  Pointwise replicability asks that two independently trained predictors, using the same random seed, agree at each fixed query with high probability.

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