A Contextual-bandit Algorithm for Mobile Context ... - Semantic Scholar

A Contextual-bandit Algorithm for Mobile ContextAware Recommender System Djallel Bouneffouf, Amel Bouzeghoub & Alda Lopes Gançarski Department of Computer Science, Télécom SudParis, UMR CNRS Samovar, 91011 Evry Cedex, France

{Djallel.Bouneffouf, Amel.Bouzeghoub, Alda.Gancarski}@itsudparis.eu

Abstract. Most existing approaches in Mobile Context-Aware Recommender Systems focus on recommending relevant items to users taking into account contextual information, such as time, location, or social aspects. However, none of them has considered the problem of user’s content evolution. We introduce in this paper an algorithm that tackles this dynamicity. It is based on dynamic exploration/exploitation and can adaptively balance the two aspects by deciding which user’s situation is most relevant for exploration or exploitation. Within a deliberately designed offline simulation framework we conduct evaluations with real online event log data. The experimental results demonstrate that our algorithm outperforms surveyed algorithms. Keywords: recommender system; machine learning; exploration/exploitation dilemma; artificial intelligence.

1

Introduction

Mobile technologies have made access to a huge collection of information, anywhere and anytime. In particular, most professional mobile users acquire and maintain a large amount of content in their repository. Moreover, the content of such repository changes dynamically, undergoes frequent insertions and deletions. In this sense, recommender systems must promptly identify the importance of new documents, while adapting to the fading value of old documents. In such a setting, it is crucial to identify interesting content for users. This problem has been addressed in recent research in the Mobile Context-Aware Recommender Systems (MCRS) area [2, 4, 5, 14]. Most of these approaches are based on the user computational behavior and his surrounding environment. Nevertheless, they do not tackle the dynamicity of the user’s content problem. The bandit algorithm is a well-known solution that addresses this problem as a need for balancing exploration/exploitation (exr/exp) tradeoff. A bandit algorithm B exploits its past experience to select documents that appear more frequently. Besides, these seemingly optimal documents may in fact be suboptimal, because of the imprecision in B’s knowledge. In order to avoid this undesired case, B has to explore doc-

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uments by choosing seemingly suboptimal documents so as to gather more information about them. Exploitation can decrease short-term user’s satisfaction since some suboptimal documents may be chosen. However, obtaining information about the documents’ average rewards (i.e., exploration) can refine B’s estimate of the documents’ rewards and in turn increases long-term user’s satisfaction. Clearly, neither a purely exploring nor a purely exploiting algorithm works well, and a good tradeoff is needed. One classical solution to the multi-armed bandit problem is the ε-greedy strategy [12]. With the probability 1-ε, this algorithm chooses the best documents based on current knowledge; and with the probability ε, it uniformly chooses any other documents uniformly. The ε parameter controls essentially the exp/exr tradeoff between exploitation and exploration. One drawback of this algorithm is that it is difficult to decide in advance the optimal value. Instead, we introduce an algorithm named Contextual-ε-greedy that achieves this goal by balancing adaptively the exp/exr tradeoff according to the user’s situation. This algorithm extends the ε-greedy strategy with an update of the exr/exp-tradeoff by selecting suitable user’s situations for either exploration or exploitation. The rest of the paper is organized as follows. Section 2 gives the key notions used throughout this paper. Section 3 reviews some related works. Section 4 presents our MCRS model and describes the algorithms involved in the proposed approach. The experimental evaluation is illustrated in Section 5. The last section concludes the paper and points out possible directions for future work.

2

Key Notions

In this section, we briefly sketch the key notions that will be of use in this paper. The user’s model: The user’s model is structured as a case based, which is composed of a set of situations with their corresponding user’s preferences, denoted U = {(S i; UPi)}, where Si is the user’s situation and UPi its corresponding user’s preferences. The user’s preferences: The user’s preferences are deduced during the user’s navigation activities, for example the number of clicks on the visited documents or the time spent on a document. Let UP be the preferences submitted by a specific user in the system at a given situation. Each document in UP is represented as a single vector d=(c1,...,cn), where ci (i=1, .., n) is the value of a component characterizing the preferences of d. We consider the following components: the total number of clicks on d, the total time spent reading d and the number of times d was recommended. Context: A user’s context C is a multi-ontology representation where each ontology corresponds to a context dimension C=(OLocation, OTime, OSocial). Each dimension models and manages a context information type. We focus on these three dimensions since they cover all needed information. These ontologies are described in [1]. Situation: A situation is an instantiation of the user’s context. We consider a situation as a triple S = (OLocation.xi, OTime.xj, OSocial.xk) where xi, xj and xk are ontology concepts or instances. Suppose the following data are sensed from the user’s mobile phone: the GPS shows the latitude and longitude of a point "48.89, 2.23"; the local time is "Oct_3_12:10_2012" and the calendar states "meeting with Paul Gerard". The corresponding situation is: S=("48.89,2.23","Oct_3_12:10_2012","Paul_Gerard"). To build

a more abstracted situation, we interpret the user’s behavior from this low-level multimodal sensor data using ontologies reasoning means. For example, from S, we obtain the following situation: Meeting=(Restaurant, Work_day, Financial_client). Among the set of captured situations, some of them are characterized as High-Level Critical Situations. High-Level Critical Situations (HLCS): A HLCS is a class of situations where the user needs the best information that can be recommended by the system, for instance, during a professional meeting. In such a situation, the system must exclusively perform exploitation rather than exploration-oriented learning. In the other case, where the user is for instance using his/her information system at home, on vacation with friends, the system can make some exploration by recommending some information ignoring his/her interest. The HLCS are predefined by the domain expert. In our case we conduct the study with professional mobile users, which is described in detail in Section 5. As examples of HLCS, we can find S1 = (restaurant, midday, client) or S2= (company, morning, manager).

3

Related Work

We refer, in the following, recent recommendation techniques that tackle the problem of making dynamic exr/exp (bandit algorithms). Existing works considering the user’s situation in recommendation are not considered in this section, refer to [1] for further information. Very frequently used in reinforcement learning to study the exr/exp tradeoff, the multi-armed bandit problem was originally described by Robbins [11]. The ε-greedy is one of the most used strategy to solve the bandit problem and was first described in [10]. The ε-greedy strategy chooses a random document with epsilon-frequency (ε), and chooses the document with the highest estimated mean otherwise. The estimation is based on the rewards observed thus far. ε must be in the interval [0, 1] and its choice is left to the user. The first variant of the ε-greedy strategy is what [6, 10] refer to as the ε-beginning strategy. This strategy makes exploration all at once at the beginning. For a given number I of iterations, documents are randomly pulled during the εI first iterations; during the remaining (1−ε)I iterations, the document of highest estimated mean is pulled. Another variant of the ε-greedy strategy is what [10] calls the ε-decreasing. In this strategy, the document with the highest estimated mean is always pulled except when a random document is pulled instead with εi frequency, where εi = {ε0/ i}, ε0 ∈]0,1] and i is the index of the current round. Besides εdecreasing, four other strategies presented [3]. Those strategies are not described here because the experiments done by [3] seem to show that ε-decreasing is always as good as the other strategies. Compared to the standard multi-armed bandit problem with a fixed set of possible actions, in MCRS, old documents may expire and new documents may frequently emerge. Therefore it may not be desirable to perform the exploration all at once at the beginning as in [6] or to decrease monotonically the effort on exploration as the decreasing strategy in [10]. As far as we know, no existing works address the problem of exr/exp tradeoff in MCRS. However few research works are dedicated to study the contextual bandit problem on recommender systems, where they consider the user’s behavior as the

context of the bandit problem. In [13], the authors extend the ε-greedy strategy by dynamically updating the ε exploration value. At each iteration, they run a sampling procedure to select a new ε from a finite set of candidates. The probabilities associated to the candidates are uniformly initialized and updated with the Exponentiated Gradient (EG) [7]. This updating rule increases the probability of a candidate ε if it leads to a user’s click. Compared to both ε-beginning and ε-decreasing, this technique gives better results. In [9], authors model the recommendation as a contextual bandit problem. They propose an approach in which a learning algorithm sequentially selects documents to serve users based on their behavior. To maximize the total number of user’s clicks, this work proposes LINUCB algorithm that is computationally efficient. As shown above, none of the mentioned works tackles both problems of exr/exp dynamicity and user’s situation consideration in the exr/exp strategy. This is precisely what we intend to do with our approach. Our intuition is that, considering the criticality of the situation when managing the exr/exp-tradeoff, improves the result of the MCRS. This strategy achieves high exploration when the current user’s situation is not critical and achieves high exploitation in the inverse case.

4

MCRS Model

In our recommender system, the recommendation of documents is modeled as a contextual bandit problem including user’s situation information [8]. Formally, a bandit algorithm proceeds in discrete trials t = 1…T. For each trial t, the algorithm performs the following tasks: Task 1: Let S t be the current user’s situation, and PS the set of past situations. The system compares S t with the situations in PS in order to choose the most similar one, S p: (1) S p= arg max sim( S t , S c )  Sc PS

The semantic similarity metric is computed by:



sim(S t ,S c ) =  j  sim j x tj ,x cj



(2)

j

In Eq.2, simj is the similarity metric related to dimension j between two concepts xjt and xjc; αj is the weight associated to dimension j (during the experimental phase, αj has a value of 1 for all dimensions). This similarity depends on how closely xj c and xjc are related in the corresponding ontology. We use the same similarity measure as [15] defined by:





sim j x tj , x cj  2 

deph( LCS ) (deph( x cj )  deph( x tj ))

(3)

In Eq. 3, LCS is the Least Common Subsumer of xjt and xjc, and deph is the number of nodes in the path from the node to the ontology root. Task 2: Let D be the document collection and Dp  D the set of documents rec-

ommended in situation S p. After retrieving S p, the system observes the user’s behavior when reading each document d p  Dp. Based on observed rewards, the algorithm chooses document d p with the greater reward r p. Task 3: After receiving the user ’s reward, the algorithm improves its documentselection strategy with the new observation: in situation S t, document d p obtains a reward rt. When a document is presented to the user and this one selects it by a click, a reward of 1 is incurred; otherwise, the reward is 0. The reward of a document is precisely its Click Through Rate (CTR). The CTR is the average number of clicks on a document by recommendation. 4.1

The ε-greedy algorithm

The ε-greedy algorithm recommends a predefined number of documents N selected using the following equation: di





argmax UC ( getCTR( d ))

if ( q  )

Random(UC )

otherwise

(4)

In Eq. 4, i∈{1,…N}, UC={d1,…,dP} is the set of documents corresponding to the user’s preferences; getCTR() computes the CTR of a given document; Random() returns a random element from a given set, allowing to perform exploration; q is a random value uniformly distributed over [0, 1] which defines the exr/exp tradeoff; ε is the probability of recommending a random exploratory document. 4.2

T h e contextual-ε-greedy algorithm

To improve the adaptation of the ε-greedy algorithm to HLCS situations, the contextual-ε-greedy algorithm compares the current user’s situation St with the HLCS class of situations. Depending on the similarity between the St and its most similar situation Sm ∈ HLCS, being B the similarity threshold (this metric is discussed below), two scenarios are possible: (1) If sim(St, Sm) ≥ B, the current situation is critical; the ε-greedy algorithm is used with ε=0 (exploitation) and St is inserted in the HLCS class of situations. (2) If sim(St, Sm) < B, the current situation is not critical; the ε-greedy algorithm is used with ε>0 (exploration) computed as indicated in Eq.5. 





 sim( S t , S m )   1   B   0

if ( sim( S t , S m ))  B otherwise

(5)

To summarize, the system does not make exploration when the current user’s situation is critical; otherwise, the system performs exploration. In this case, the degree of exploration decreases when the similarity between St and Sm increases.

5

Experimental Evaluation

In order to empirically evaluate the performance of our approach, and in the absence of a standard evaluation framework, we propose an evaluation framework based on a diary set of study entries. The main objectives of the experimental evaluation are: (1) to find the optimal threshold B value described in Section 4.2 and (2) to evaluate the performance of the proposed algorithm (contextual-ε-greedy). In the following, we describe our experimental datasets and then present and discuss the obtained results. We have conducted a diary study with the collaboration of the French software company Nomalys1. This company provides a history application, which records the time, current location, social and navigation information of its users during their application use. The diary study has taken 18 months and has generated 178 369 diary situation entries. Each diary situation entry represents the capture, of contextual time, location and social information. For each entry, the captured data are replaced with more abstracted information using time, spatial and social ontologies [1]. From the diary study, we have obtained a total of 2 759 283 entries concerning the user’s navigation, expressed with an average of 15.47 entries per situation. In order to set out the threshold similarity value, we use a manual classification as a baseline and compare it with the results obtained by our technique. So, we take a random sampling of 10% of the situation entries, and we manually group similar situations; then we compare the constructed groups with the results obtained by our similarity algorithm, with different threshold values.

Fig. 1.

Effect of B threshold value on the similarity precision

Fig. 1 shows the effect of varying the threshold situation similarity parameter B in the interval [0, 3] on the overall precision. Results show that the best performance is obtained when B has the value 2.4 achieving a precision of 0.849. Consequently, we use the optimal threshold value B = 2.4 for testing our MCRS. To test the proposed contextual-ε-greedy algorithm, we firstly have collected 3000 situations with an occurrence greater than 100 to be statistically meaningful. Then, we have sampled 10000 documents that have been shown on any of these situations. The testing step consists of evaluating the algorithms for each testing situation using the average CTR. The average CTR for a particular iteration is the ratio between the total 1

Nomalys is a company that provides a graphical application on Smartphones allowing users to access their company’s data.

number of clicks and the total number of displays. Then, we calculate the average CTR over every 1000 iterations. The number of documents (N) returned by the recommender system for each situation is 10 and we have run the simulation until the number of iterations reaches 10000, which is the number of iterations where all algorithms have converged. In the first experiment, in addition to a pure exploitation baseline, we have compared our algorithm to the algorithms described in the related work (Section 3): ε-greedy; ε-beginning, ε-decreasing and EG. In Fig. 2, the horizontal axis is the number of iterations and the vertical axis is the performance metric.

Fig. 2. Average CTR for exr/exp algorithms We have parameterized the different algorithms as follows: ε-greedy was tested with two parameter values: 0.5 and 0.9; ε-decreasing and EG use the same set {εi = 1- 0.01 * i, i = 1,...,100}; ε-decreasing starts using the highest value and reduces it by 0.01 every 100 iterations, until it reaches the smallest value. Overall tested algorithms have better performance than the baseline. However, for the first 2000 iterations, with pure exploitation, the exploitation baseline achieves a faster increase convergence. But in the long run, all exr/exp algorithms improve the average CTR at convergence. We have several observations regarding the different exr/exp algorithms. For the εdecreasing algorithm, the converged average CTR increases as the ε decreases (exploitation augments). For the ε-greedy(0.9) and ε-greedy(0.5), even after convergence, the algorithms still give respectively 90% and 50% of the opportunities to documents having low average CTR, which decreases significantly their results. While the EG algorithm converges to a higher average CTR, its overall performance is not as good as ε-decreasing. Its average CTR is low at the early step because of more exploration, but does not converge faster. The contextual-ε-greedy algorithm effectively learns the optimal ε; it has the best convergence rate, increases the average CTR by a factor of 2 over the baseline and outperforms all other exr/exp algorithms. The improvement comes from a dynamic tradeoff between exr/exp, controlled by the critical situation (HLCS) estimation. At the early stage, this algorithm takes full advantage of exploration without wasting opportunities to establish good results.

6

Conclusion

In this paper, we study the problem of exploitation and exploration in mobile contextaware recommender systems and propose a novel approach that balances adaptively

exr/exp regarding the user’s situation. In order to evaluate the performance of the proposed algorithm, we compare it with other standard exr/exp strategies. The experimental results demonstrate that our algorithm performs better on average CTR in various configurations. In the future, we plan to evaluate the scalability of the algorithm on-board a mobile device and investigate other public benchmarks.

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