Linear submodular bandits with a knapsack constraint

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Conference Proceeding
30th AAAI Conference on Artificial Intelligence, AAAI 2016, 2016, pp. 1380 - 1386
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© 2016, Association for the Advancement of Artificial Intelligence ( All rights reserved. Linear submodular bandits has been proven to be effective in solving the diversification and feature-based exploration problems in retrieval systems. Concurrently, many web-based applications, such as news article recommendation and online ad placement, can be modeled as budget-limited problems. However, the diversification problem under a budget constraint has not been considered. In this paper, we first introduce the budget constraint to linear submodular bandits as a new problem called the linear submodular bandits with a knapsack constraint. We then define an α-approximation unit-cost regret considering that submodular function maximization is NP-hard. To solve this problem, we propose two greedy algorithms based on a modified UCB rule.We then prove these two algorithms with different regret bounds and computational costs. We also conduct a number of experiments and the experimental results confirm our theoretical analyses.
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