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We study the collaborative PAC learning problem recently proposed in Blum etal.~\cite{BHPQ17}, in which we have $k$ players and they want to learn a targetfunction collaboratively, such that the learned function approximates thetarget function well on all players' distributions simultaneously. The qualityof the collaborative learning algorithm is measured by the ratio between thesample complexity of the algorithm and that of the learning algorithm for asingle distribution (called the overhead). We obtain a collaborative learningalgorithm with overhead $O(\ln k)$, improving the one with overhead $O(\ln^2k)$ in \cite{BHPQ17}. We also show that an $\Omega(\ln k)$ overhead isinevitable when $k$ is polynomial bounded by the VC dimension of the hypothesisclass. Finally, our experimental study has demonstrated the superiority of ouralgorithm compared with the one in Blum et al. on real-world datasets.

Tight Bounds for Collaborative PAC Learning via Multiplicative Weights