Many learning tasks, such as regression and classification, are usually framed that way [1]. When N 1, computing the gradient of the objective in(1) becomes a bottleneck, even if individual gradients θL(zi,θ) are cheap to evaluate. For a fixed computational budget, itisthustempting toreplace vanilla gradient descent bymore iterations but using anapproximate gradient, obtained using only afewdata points. Stochastic gradient descent (SGD; [2]) follows this template.

We extend our results to the general case of maximizing a monotone submodular function subject to the intersection of a p-set system and multiple knapsack constraints. Finally, we evaluate the performance of our algorithms on multiple real-lifeapplications, includingmovierecommendation, locationsummarization, Twittertextsummarization,andvideosummarization.