Abstract: We study a recent model of collaborative PAC learning where $k$ players with $k$ different tasks collaborate to learn a single classifier that works for all tasks. Previous work showed that when there is a classifier that has very small error on all tasks, there is a collaborative algorithm that finds a single classifier for all tasks and has $O((\ln (k))^2)$ times the worst-case sample complexity for learning a single task. In this work, we design new algorithms for both the realizable and the non-realizable setting, having sample complexity only $O(\ln (k))$ times the worst-case sample complexity for learning a single task. The sample complexity upper bounds of our algorithms match previous lower bounds and in some range of parameters are even better than previous algorithms that are allowed to output different classifiers for different tasks.