The majority of recommender systems are designed to recommend items (such as movies and products) to users. We focus on the problem of recommending buyers to sellers which comes with new challenges: (1) constraints on the number of recommendations buyers are part of before they become overwhelmed, (2) constraints on the number of recommendations sellers receive within their budget, and (3) constraints on the set of buyers that sellers want to receive (e.g., no more than two people from the same household). We propose the following critical problems of recommending buyers to sellers: Constrained Recommendation (C-REC) capturing the first two challenges, and Conflict-Aware Constrained Recommendation (CAC-REC) capturing all three challenges at the same time. We show that C-REC can be modeled using linear programming and can be efficiently solved using modern solvers. On the other hand, we show that CAC-REC is NP-hard. We propose two approximate algorithms to solve CAC-REC and show that they achieve close to optimal solutions via comprehensive experiments using real-world datasets.
Xie, Lakshmanan, and Wood in @cite_4 study the problem of composite recommendations, where each recommendation comprises a set of items. They also consider constraints including the number of items that can be recommended to a user. Their objective, however, is to minimize the cost of a recommended set of items when each item has a price to be paid.
@cite_4
2010127467 2962847184 2079728196 2951177685
Classical recommender systems provide users with a list of recommendations where each recommendation consists of a single item, e.g., a book or DVD. However, several applications can benefit from a system capable of recommending packages of items, in the form of sets. Sample applications include travel planning with a limited budget (price or time) and twitter users wanting to select worthwhile tweeters to follow given that they can deal with only a bounded number of tweets. In these contexts, there is a need for a system that can recommend top-k packages for the user to choose from. Motivated by these applications, we consider composite recommendations, where each recommendation comprises a set of items. Each item has both a value (rating) and a cost associated with it, and the user specifies a maximum total cost (budget) for any recommended set of items. Our composite recommender system has access to one or more component recommender system, focusing on different domains, as well as to information sources which can provide the cost associated with each item. Because the problem of generating the top recommendation (package) is NP-complete, we devise several approximation algorithms for generating top-k packages as recommendations. We analyze their efficiency as well as approximation quality. Finally, using two real and two synthetic data sets, we subject our algorithms to thorough experimentation and empirical analysis. Our findings attest to the efficiency and quality of our approximation algorithms for top-k packages compared to exact algorithms. Most recommender systems recommend a list of items. The user examines the list, from the first item to the last, and often chooses the first attractive item and does not examine the rest. This type of user behavior can be modeled by the cascade model. In this work, we study cascading bandits, an online learning variant of the cascade model where the goal is to recommend K most attractive items from a large set of L candidate items. We propose two algorithms for solving this problem, which are based on the idea of linear generalization. The key idea in our solutions is that we learn a predictor of the attraction probabilities of items from their features, as opposing to learning the attraction probability of each item independently as in the existing work. This results in practical learning algorithms whose regret does not depend on the number of items L. We bound the regret of one algorithm and comprehensively evaluate the other on a range of recommendation problems. The algorithm performs well and outperforms all baselines. Improving recommendation accuracy is the mostly focused target of recommendation systems, while it has been increasingly recognized that accuracy is not enough as the only quality criterion. More concepts have been proposed recently to augment the evaluation dimensions, such as similarity, diversity, long-tail, etc. Simultaneously considering multiple criteria leads to a multi-task recommendation. In this paper, a graph-based recommendation approach is proposed to effectively and flexibly trade-off among them. Our approach is considered based a 1st order Markovian graph with transition probabilities between user-item pairs. A "cost flow" concept is proposed over the graph, so that items with lower costs are stronger recommended to a user. The cost flows are formulated in a recursive dynamic form, whose stability is proved to be guaranteed by appropriately lower-bounding the transition costs. Furthermore, a mixture of transition costs is designed by combining three ingredients related to long-tail, focusing degree and similarity. To evaluate the ingredients, we propose an orthogonal-sparse-orthogonal nonnegative matrix tri-factorization model and an efficient multiplicative algorithm. Empirical experiments on real-world data show promising results of our approach, which could be regarded as a general framework for other affects if transition costs are designed in various ways. We consider online resource allocation problems where given a set of requests our goal is to select a subset that maximizes a value minus cost type of objective function. Requests are presented online in random order, and each request possesses an adversarial value and an adversarial size. The online algorithm must make an irrevocable accept reject decision as soon as it sees each request. The "profit" of a set of accepted requests is its total value minus a convex cost function of its total size. This problem falls within the framework of secretary problems. Unlike previous work in that area, one of the main challenges we face is that the objective function can be positive or negative and we must guard against accepting requests that look good early on but cause the solution to have an arbitrarily large cost as more requests are accepted. This requires designing new techniques. We study this problem under various feasibility constraints and present online algorithms with competitive ratios only a constant factor worse than those known in the absence of costs for the same feasibility constraints. We also consider a multi-dimensional version of the problem that generalizes multi-dimensional knapsack within a secretary framework. In the absence of any feasibility constraints, we present an O(l) competitive algorithm where l is the number of dimensions; this matches within constant factors the best known ratio for multi-dimensional knapsack secretary.