Knapsack Constrained Contextual Submodular List Prediction with Application to Multi-document Summarization

We study the problem of predicting a set or list of options under knapsack constraint. The quality of such lists are evaluated by a submodular reward function that measures both quality and diversity. Similar to DAgger (Ross et al., 2010), by a reduction to online learning, we show how to adapt two sequence prediction models to imitate greedy maximization under knapsack constraint problems: CONSEQOPT (Dey et al., 2012a) and SCP (Ross et al., 2013). Experiments on extractive multi-document summarization show that our approach outperforms existing state-of-the-art methods.