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Product ranking is the core problem for revenue-maximizing online retailers.To design proper product ranking algorithms, various consumer choice models areproposed to characterize the consumers' behaviors when they are provided with alist of products. However, existing works assume that each consumer purchasesat most one product or will keep viewing the product list after purchasing aproduct, which does not agree with the common practice in real scenarios. Inthis paper, we assume that each consumer can purchase multiple products atwill. To model consumers' willingness to view and purchase, we set a randomattention span and purchase budget, which determines the maximal amount ofproducts that he/she views and purchases, respectively. Under this setting, wefirst design an optimal ranking policy when the online retailer can preciselymodel consumers' behaviors. Based on the policy, we further develop theMultiple-Purchase-with-Budget UCB (MPB-UCB) algorithms with $\~O(\sqrt{T})$regret that estimate consumers' behaviors and maximize revenue simultaneouslyin online settings. Experiments on both synthetic and semi-synthetic datasetsprove the effectiveness of the proposed algorithms.

Product Ranking for Revenue Maximization with Multiple Purchases