We investigate the computational efficiency of multitask learning of Boolean functions over the $d$-dimensional hypercube, that are related by means of a feature representation of size $k \ll d$ shared across all tasks. We present a polynomial time multitask learning algorithm for the concept class of halfspaces with margin $\gamma$, which is based on a simultaneous boosting technique and requires only $\textrm{poly}(k/\gamma)$ samples-per-task and $\textrm{poly}(k\log(d)/\gamma)$ samples in total. In addition, we prove a computational separation, showing that assuming there exists a concept class that cannot be learned in the attribute-efficient model, we can construct another concept class such that can be learned in the attribute-efficient model, but cannot be multitask learned efficiently -- multitask learning this concept class either requires super-polynomial time complexity or a much larger total number of samples.

翻译：我们用所有任务共享的大小 $k =ll d$ 的特征表示,调查多任务学习在美元维度超立方体上的布林函数的计算效率。 我们为概念类半空提供多任务学习算法, 边值为$\gamma$, 以同步提振技术为基础, 只需要 $\ textrm{poly} (k/\gamma) $ text- per- task 和 $\ textrm{poly} (k\log (d)/\ gamma) $ 样本。 此外, 我们证明一个计算分离, 表明假设存在在属性效率模型中无法学习的概念类, 我们可以构建另一个概念类, 这样可以在属性效率模型中学习, 但是不能是多任务类学习效率 -- 多任务类学习这个概念类, 要么需要超极时间复杂性, 要么需要更多样本。