jmlr jmlr2005 jmlr2005-12 knowledge-graph by maker-knowledge-mining

12 jmlr-2005-An MDP-Based Recommender System

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Author: Guy Shani, David Heckerman, Ronen I. Brafman

Abstract: Typical recommender systems adopt a static view of the recommendation process and treat it as a prediction problem. We argue that it is more appropriate to view the problem of generating recommendations as a sequential optimization problem and, consequently, that Markov decision processes (MDPs) provide a more appropriate model for recommender systems. MDPs introduce two beneﬁts: they take into account the long-term effects of each recommendation and the expected value of each recommendation. To succeed in practice, an MDP-based recommender system must employ a strong initial model, must be solvable quickly, and should not consume too much memory. In this paper, we describe our particular MDP model, its initialization using a predictive model, the solution and update algorithm, and its actual performance on a commercial site. We also describe the particular predictive model we used which outperforms previous models. Our system is one of a small number of commercially deployed recommender systems. As far as we know, it is the ﬁrst to report experimental analysis conducted on a real commercial site. These results validate the commercial value of recommender systems, and in particular, of our MDP-based approach. Keywords: recommender systems, Markov decision processes, learning, commercial applications

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 IL Computer Science Department Ben-Gurion University Beer-Sheva, Israel 84105 Editor: Craig Boutilier Abstract Typical recommender systems adopt a static view of the recommendation process and treat it as a prediction problem. [sent-9, score-0.713]

2 We argue that it is more appropriate to view the problem of generating recommendations as a sequential optimization problem and, consequently, that Markov decision processes (MDPs) provide a more appropriate model for recommender systems. [sent-10, score-0.858]

3 To alleviate this problem, many web sites attempt to help users by incorporating a recommender system (Resnick and Varian, 1997) that provides users with a list of items and/or webpages that are likely to interest them. [sent-20, score-1.231]

4 Once the user makes her choice, a new list of recommended items is presented. [sent-21, score-0.679]

5 In particular, an optimal policy will take into account the likelihood of a recommendation to be accepted by the user, the immediate value to the site of such an acceptance, and the long-term implications of this on the user’s future choices. [sent-38, score-0.574]

6 The approach we suggest initializes a predictive model of user behavior using data gathered on the site prior to the implementation of the recommender system. [sent-52, score-1.013]

7 The predictive model we describe is motivated by our sequential view of the recommendation process, but constitutes an independent contribution. [sent-56, score-0.537]

8 That is, the system is trained using historical data from sites that do not provide recommendations, and tested to see whether the recommendations conform to actual user behavior. [sent-65, score-0.627]

9 However, predictive accuracy is not an ideal measure, as it does not test how user behavior is inﬂuenced by the system’s suggestions or what percentage of recommendations are accepted by users. [sent-67, score-0.709]

10 These results, which to the best of our knowledge are among the ﬁrst reports of online performance in a commercial site, are reported in Section 6, providing very encouraging validation to recommender systems in general, and to our sequential optimization approach in particular. [sent-75, score-0.562]

11 In Section 5 we explain how we use this predictive model as a basis for a more sophisticated MDP-based model for the recommender system. [sent-89, score-0.634]

12 Many web sites presenting a wide variety of content (such as articles, news stories, or items to purchase) discovered that users had difﬁculties ﬁnding the items that interested them out of the total selection. [sent-96, score-0.898]

13 Recommender Systems (Resnick and Varian, 1997) help users limit their search by supplying a list of items that might interest a speciﬁc user. [sent-97, score-0.535]

14 Different approaches were suggested for supplying meaningful recommendations to users and some were implemented in modern sites (Schafer et al. [sent-98, score-0.528]

15 Approaches originating from the ﬁeld of information retrieval (IR) rely on the content of the items (such as description, category, title, author) and therefore are known as content-based recommendations (Mooney and Roy, 2000). [sent-103, score-0.677]

16 Based on this score, a list of items similar to the ones the user previously selected can be supplied. [sent-105, score-0.6]

17 Knowledge-based recommender systems (Burke, 2000) go one step farther by using deeper knowledge about the user and the domain. [sent-106, score-0.645]

18 2 Collaborative Filtering The collaborative ﬁltering approach originates in human behavior: people searching for an interesting item they know little of, such as a movie to rent at the video store, tend to rely on friends to recommend items they tried and liked. [sent-114, score-0.657]

19 Over the net however, a larger community that can recommend items to our user is available, but the persons in this large community know little or nothing about each other. [sent-116, score-0.605]

20 Conceptually, the goal of a collaborative ﬁltering engine is to identify those users whose taste in items is predictive of the taste of a certain person (usually called a neighborhood), and use their recommendations to construct a list of items interesting for her. [sent-117, score-1.43]

21 A binary grading method is used when a value of 1 is given to items the user has bought and 0 to other items. [sent-125, score-0.638]

22 Given the selections of a given user, a memory-based system identiﬁes similar users and makes recommendations based on the items selected by these users. [sent-139, score-0.869]

23 3 The Sequential Nature of the Recommendation Process Most recommender systems work in a sequential manner: they suggest items to the user who can then accept one of the recommendations. [sent-146, score-1.05]

24 This sequential nature of the recommendation process, where at each stage a new list is calculated based on the user’s past ratings, will lead us naturally to our reformulation of the recommendation process as a sequential optimization process. [sent-148, score-0.773]

25 Namely, optimal recommendations may depend not only on previous items pruchased, but also on the order in which those items are purchased. [sent-150, score-1.016]

26 In the context of recommender systems, if we equate actions with recommendations, then an MDP can be used to model user behavior with recommendations – as we show below – whereas an MC can be used to model user behavior without recommendations. [sent-216, score-1.296]

27 The Predictive Model Our ﬁrst step is to construct a predictive model of user purchases, that is, a model that can predict what item the user will buy next. [sent-227, score-0.937]

28 In Section 4 we shall 1271 S HANI , B RAFMAN AND H ECKERMAN show that our predictive model outperforms previous models, and in Section 5 we shall intialize our MDP-based recommender system using this predictive model. [sent-230, score-0.784]

29 Evaluation of the Predictive Model Before incorporating our predictive model into an MDP-based recommender system, we evaluated the accuracy of the predictive model. [sent-316, score-0.75]

30 Two data sets were used: one containing user transactions (purchases) and one containing user browsing paths obtained from web logs. [sent-324, score-0.52]

31 We ﬁltered out items that were bought/visited less than 100 times and users who bought/browsed no more than one item as is commonly done when evaluating predictive models (for example, Zimdars et al. [sent-325, score-0.872]

32 We were left with 116 items and 10820 users in the transactions data set, and 65 items and 6678 users in the browsing data set. [sent-327, score-1.038]

33 1 R ECOMMENDATION S CORE For this measure of accuracy, a recommendation is deemed successful if the observed item ti is among the top m recommended items (m is varied in the experiments). [sent-355, score-0.936]

34 This score is meaningful for commerce sites that require a short list of recommendations and therefore care little about the ordering of the items in the list. [sent-358, score-0.802]

35 There are more items and users in the transaction data set since we used transactions over one year, whereas browsing data was collected only during one week. [sent-360, score-0.562]

36 2 E XPONENTIAL D ECAY S CORE This measure of accuracy is based on the position of the observed ti on the recommendation list, thus evaluating not only the content of the list but also the order of items in it. [sent-363, score-0.69]

37 In particular, it is assumed that a user will actually see the mth item in the list with probability p(m) = 2−(m−1)/(α−1) , (m ≥ 1) (11) where α is the half-life parameter—the index of the item in the list with probability 0. [sent-365, score-0.709]

38 ,ti−1 is a case, and pos(ti |c) is the position of the observed item ti in the list of recommended items for c. [sent-370, score-0.683]

39 In the non-sequential approach, for every item, a decision tree is built that predicts whether the item will be selected based on whether the remaining items were or were not selected. [sent-385, score-0.544]

40 In the sequential approach, for every item, a decision tree is built that predicts whether the item will be selected next, based on the previous k items that were selected. [sent-386, score-0.61]

41 In either 1278 A N MDP-BASED R ECOMMENDER S YSTEM case, once recommendations are available in the site (thus changing the site structure), skipping may prove beneﬁcial. [sent-432, score-0.775]

42 We assume that we are given a set of cases describing user behavior within a site that does not provide recommendations, as well as a probabilistic predictive model of a user acting without recommendations generated from this data. [sent-437, score-1.126]

43 The predictive model provides the probability the user will purchase a particular item x given that her sequence of past purchases is x1 , . [sent-439, score-0.73]

44 The states of the MDP for our recommender system are k-tuples of items (for example, books, CDs), some preﬁx of which may contain null values corresponding to missing items. [sent-454, score-0.839]

45 Because the state encodes the list of items purchased, the reward depends on the last item deﬁning the current state only. [sent-459, score-0.745]

46 For example, the reward for state x1 , x2 , x3 is the reward generated by the site from the sale of item x3 . [sent-460, score-0.537]

47 When we recommend an item x , the user has three options: • Accept this recommendation, thus transferring from state x1 , x2 , x3 into x2 , x3 , x • Select some non-recommended item x , thus transferring the state x1 , x2 , x3 into x2 , x3 , x . [sent-463, score-0.78]

48 The transition function for the MDP model: 1 trMDP ( x1 , x2 , x3 , x , x2 , x3 , x ) (13) 1279 S HANI , B RAFMAN AND H ECKERMAN is the probability that the user will select item x given that item x is recommended in state 1 x1 , x2 , x3 . [sent-466, score-0.863]

49 We write trMDP to denote that only single item recommendations are used. [sent-467, score-0.543]

50 A for-proﬁt e-commerce8 site is unlikely to use a recommender system that generates irrelevant recommendations for a long period, while waiting for it to converge to an optimal policy. [sent-472, score-0.956]

51 We can do so based on any good predictive model, making the following assumptions: • A recommendation increases the probability that a user will buy an item. [sent-474, score-0.736]

52 • The probability that a user will buy an item that was not recommended is lower than the probability that she will buy when the system issues no recommendations at all, but still proportional to it. [sent-478, score-1.027]

53 We use tr predict (s, s · r) to denote the probability that the user will choose r next, given that its current state is s according to the predictive model in which recommendations are not considered, that is, Pr pred (r|s). [sent-487, score-0.852]

54 Actually CF models do not refer to the presence of recommendations, but using such systems to generate recommendations to users in commercial applications has the underlying assumption that the recommendation will increase the likelihood that a user will purchase an item. [sent-493, score-1.163]

55 (2000), who showed that the increase in the probability of following a recommendation is large when one recommends items having high lift, deﬁned to be pr(x|h) . [sent-498, score-0.668]

56 It seems reasonable that, as the list of recommendations grows, the probability of selecting any item decreases. [sent-511, score-0.581]

57 Such a policy will, in effect, tell us what item to recommend given any sequence of user purchases. [sent-521, score-0.592]

58 Moreover, in the web site implementation, it is easy enough to ﬁlter out items that were already bought by the user from our list of recommendations. [sent-530, score-0.868]

59 This approximation, although risky in general MDPs, is motivated by the fact that in our initial model, for each state there is a relatively small number of items that are likely to be selected; and the probability of making a transition into an un-encountered state is very low. [sent-559, score-0.562]

60 The number of possible recommendations is nκ , where n is the number of items and κ is the number of items we recommend each time. [sent-569, score-1.059]

61 Recall that we assumed that the probability that a user buys a particular item depends on her current state, the item, and whether or not this item is recommended. [sent-571, score-0.633]

62 The complexity of ﬁnding an optimal policy when recommending multiple items at each stage under our assumptions remains the same as the complexity of computing an optimal policy for single item recommendations. [sent-593, score-0.818]

63 In particular, the system does not recommend items that are likely to be bought whether recommended or not, but rather recommends items whose likelihood of being purchased is increased when they are recommended. [sent-595, score-1.025]

64 Nonetheless, when recommendations are based solely on lift, it is possible that many recommendations will be made for which the absolute probability of a purchase (or click) is small. [sent-596, score-0.733]

65 The site need only keep track of the recommendations and the user selections and, say, once a week use those statistics to build a new model and replace it with the old one. [sent-607, score-0.755]

66 • cout (s, r, s · r)—the number of times the user took item r in state s even though it was not recommended, • ctotal (s, s · r)—the number of times a user took item r while being in state s, regardless of whether it was recommended or not. [sent-610, score-1.039]

67 This, in turn, requires that for each state s and for every recommendation r, we observe the response of users to a recommendation of r in state s sufﬁciently many times. [sent-619, score-0.844]

68 If at each state the system always returns the best recommendations only, then most values for count(s, r, s · r) would be 0, because most items will not appear among the best recommendations. [sent-620, score-0.763]

69 Another possible solution is to show the best recommendation on the top of the list, but show items less likely to be purchased as the second and third items on the list. [sent-629, score-1.046]

70 In our implementation we use a list of three recommendations where the ﬁrst one is always the optimal one, but the second and third items are selected using the Boltzman distribution without a cutoff. [sent-630, score-0.715]

71 When new items are added, users will start buying them and positive counts for them will appear. [sent-632, score-0.523]

72 1286 A N MDP-BASED R ECOMMENDER S YSTEM insert deleted items into the list of recommended items – an undesirable feature. [sent-642, score-0.795]

73 We compare the performance of our MDP-based recommender system (denoted MDP) with the performance of a recommender system based on our predictive model (denoted MC) as well as other variants. [sent-649, score-1.092]

74 Users received recommendations when adding items to the shopping cart. [sent-659, score-0.677]

75 12 The recommendations were based on the last k items added to the cart ordered by the time they were added. [sent-660, score-0.677]

76 Every time a user was presented with a list of recommendations on either page, the system stored the recommendations that were presented and recorded whether the user purchased a recommended item. [sent-662, score-1.33]

77 As discussed above, a predictive model can answer queries in the form Pr(x|h)—the probability that item x will be purchased given user history h. [sent-672, score-0.691]

78 Users also received recommendations when looking at the description of a book, but these recommendations where based only on the user’s visit to the current page and not on her cart. [sent-678, score-0.676]

79 We compared four policies, where the ﬁrst policy uses information about the effect of recommendations, and the remaining policies are based on the predictive model solely: • Optimal – recommends items based on optimal policy for the MDP. [sent-684, score-0.82]

80 • Greedy – recommends items that maximize Pr(x|h) · R(x) (where Pr(x|h) is the probability of buying item x given user history h, and R(x) is the value of x to the site – for example, net proﬁt). [sent-685, score-1.019]

81 The length of user session was taken from the learned distribution of user session length in the actual site. [sent-690, score-0.524]

82 Based on the last bit of this cart-id, the user was provided with recommendations by the MDP or MC. [sent-704, score-0.561]

83 7% of the users who made at least one purchase were shown MDP-based recommendations and the other 49. [sent-714, score-0.553]

84 The ﬁrst item was excluded as it was bought without the beneﬁt of recommendations, and is therefore irrelevant to the comparison between the recommender systems. [sent-717, score-0.703]

85 This is not entirely accurate as the site also provides recommendations for items in the book description page. [sent-723, score-0.878]

86 We used the one-tailed version of the test as the directional hypothesis that the MDP recommender is better than the MC recommender has been theoretically motivated above. [sent-729, score-0.844]

87 In our experiment, the average number of items bought per user session was 6. [sent-736, score-0.677]

88 15), whereas the average price of items was 4% higher in favor of the MDP-based recommender (p = 0. [sent-738, score-0.761]

89 In our second and last experiment, we compared site performance with and without a recommender system. [sent-741, score-0.584]

90 Fortunately, the site owner was willing to remove the recommender system from the site for one week. [sent-744, score-0.78]

91 Thus, we were able to compare average proﬁts per user session during two consecutive weeks – one with recommendations and one without recommendations. [sent-745, score-0.6]

92 18 We found that, when the recommender system was not in use, average site proﬁt dropped 17% (p = 0. [sent-746, score-0.618]

93 Overall, our experiments support the claims concerning the added value of using recommendations in commercial web sites and the validity of the MDP-based model for recommender systems. [sent-749, score-0.928]

94 If recommendation latency is noticeable, no reasonable site administrator will use the recommender system. [sent-757, score-0.875]

95 Table 5 shows the number of recommendations generated per second by the recommender system. [sent-758, score-0.76]

96 We display recommendations between 3/27/2003 and 4/3/2003, and without recommendations from 3/19/2003 to 3/26/2003. [sent-763, score-0.676]

97 Our work presents one of a few examples of commercial systems that use MDPs, and one of the ﬁrst reports of the performance of commercially deployed recommender system. [sent-781, score-0.543]

98 Our experimental results validate both the utility of recommender systems and the utility of the MDP-based approach to recommender systems. [sent-782, score-0.882]

99 Our predictive model should also make use of relations between items that can be explicitly speciﬁed. [sent-799, score-0.519]

100 For example, most sites that sell items have a large catalogue with hierarchical structure such as categories or subjects, a carefully constructed web structure, and item properties such as author name. [sent-800, score-0.606]

similar papers computed by tfidf model

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