Sample-Optimal Agnostic Boosting with Unlabeled Data

Boosting provides a practical and provably effective framework for constructing accurate learning algorithms from inaccurate rules of thumb. It extends the promise of sample-efficient learning to settings where direct Empirical Risk Minimization (ERM) may not be implementable efficiently. In the realizable setting, boosting is known to offer this computational reprieve without compromising on sample efficiency. However, in the agnostic case, existing boosting algorithms fall short of achieving the optimal sample complexity. We highlight a previously unexplored avenue of improvement: unlabeled samples. We design a computationally efficient agnostic boosting algorithm that matches the sample complexity of ERM, given polynomially many additional unlabeled samples. In fact, we show that the total number of samples needed, unlabeled and labeled inclusive, is never more than that for the best known agnostic boosting algorithm -so this result is never worse -while only a vanishing fraction of these need to be labeled for the algorithm to succeed. This is particularly fortuitous for learningtheoretic applications of agnostic boosting, which often take place in the distribution-specific setting, where unlabeled samples can be availed for free. We also prove that the resultant guarantee is resilient against mismatch between the distributions governing the labeled and unlabeled samples. Finally, we detail an application of this result in reinforcement learning.