Tight Bounds for Collaborative PAC Learning via Multiplicative Weights
This work improves efficiency for distributed machine learning systems where multiple players need to learn a shared function, though it is incremental over prior results.
The paper tackles the collaborative PAC learning problem by developing an algorithm that reduces the overhead from O(ln^2 k) to O(ln k), and proves a lower bound of Ω(ln k) for polynomial k relative to VC dimension, with experiments showing superiority on real-world datasets.
We study the collaborative PAC learning problem recently proposed in Blum et al.~\cite{BHPQ17}, in which we have $k$ players and they want to learn a target function collaboratively, such that the learned function approximates the target function well on all players' distributions simultaneously. The quality of the collaborative learning algorithm is measured by the ratio between the sample complexity of the algorithm and that of the learning algorithm for a single distribution (called the overhead). We obtain a collaborative learning algorithm with overhead $O(\ln k)$, improving the one with overhead $O(\ln^2 k)$ in \cite{BHPQ17}. We also show that an $Ω(\ln k)$ overhead is inevitable when $k$ is polynomial bounded by the VC dimension of the hypothesis class. Finally, our experimental study has demonstrated the superiority of our algorithm compared with the one in Blum et al. on real-world datasets.