adfa, p. 1, 2011.

© Springer-Verlag Berlin Heidelberg 2011

A Contextual-bandit Algorithm for Mobile Context-

Aware 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}@it-

sudparis.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, rec-

ommender 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 identi-

fy 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, 19, 20].

Most of these approaches are based on the user computational behavior and his sur-

rounding 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 fre-

quently. Besides, these seemingly optimal documents may in fact be suboptimal, be-

cause of the imprecision in B’s knowledge. In order to avoid this undesired case, B

has to explore documents by choosing seemingly suboptimal documents so as to

gather more information about them. Exploitation can decrease short-term user’s sat-

isfaction since some suboptimal documents may be chosen. However, obtaining in-

formation 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 satisfac-

tion. 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 prob-

lem 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 algo-

rithm is that it is difficult to decide in advance the optimal value. Instead, we intro-

duce 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 ex-

tends 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 pa-

per 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 = {(Si;

UPi)}, where S

i is the user’s situation and UP

i its corresponding user’s preferences.

The user’s preferences: The user’s preferences are deduced during the user’s naviga-

tion 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 prefer-

ences 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 mod-els and manages a context information type. We focus on these three dimensions since they cover all needed information. These ontologies are described in [1, 16]. 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 corre-sponding 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 multi-modal 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 con-duct 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 mul-

ti-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 be-

ginning. 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 ε-

decreasing, 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 associat-

ed 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 criticali-

ty 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 con-

textual 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 St be the current user’s situation, and PS the set of past situations.

The system compares St

with the situations in PS in order to choose the most

similar one, Sp:

),(maxarg

cS

ctp SSsim=S

PS

(1)

The semantic similarity metric is computed by:

j

c

j

t

jjj

ct ,xxsim) =,Ssim(S (2)

In Eq.2, simj is the similarity metric related to dimension j between two concepts xj

t and xj

c; 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 xj

c are related in the corresponding ontology. We use the same

similarity measure as [15, 17, 18] defined by:

))()((

)(2,

t

j

c

j

c

j

t

jjxdephxdeph

LCSdephxxsim

(3)

In Eq. 3, LCS is the Least Common Subsumer of xjt and xj

c, 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 DpD the set of documents rec-

ommended in situation Sp. After retrieving S

p, the system observes the user’s

behavior when reading each document dp Dp. Based on observed rewards, the algorithm chooses document dp with the greater reward rp.

Task 3: After receiving the user ’s reward, the algorithm improves its document-selection strategy with the new observation: in situation S

t, document dp 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:

)())((argmax

)(

qifdgetCTR

otherwiseUCRandomd

UC

i (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() re-

turns a random element from a given set, allowing to perform exploration; q is a ran-

dom value uniformly distributed over [0, 1] which defines the exr/exp tradeoff; ε is

the probability of recommending a random exploratory document.

4.2 The 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, S

m) ≥ 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, S

m) < B, the current situation is not critical; the ε-greedy algorithm is

used with ε>0 (exploration) computed as indicated in Eq.5.

BSSsimifB

SSsim

otherwise

mtmt

)),((

),(1

0

(5)

To summarize, the system does not make exploration when the current user’s situa-

tion is critical; otherwise, the system performs exploration. In this case, the degree of

exploration decreases when the similarity between St and S

m 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 ap-

plication 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 navi-

gation, 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 situ-

ations; then we compare the constructed groups with the results obtained by our simi-

larity 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 ob-

tained 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

1 Nomalys is a company that provides a graphical application on Smartphones allowing users to

access their company’s data.

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

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 rec-

ommender 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 algo-

rithms have converged. In the first experiment, in addition to a pure exploitation base-

line, 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 ε-

decreasing algorithm, the converged average CTR increases as the ε decreases (ex-

ploitation augments). For the ε-greedy(0.9) and ε-greedy(0.5), even after conver-

gence, 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 ad-

vantage of exploration without wasting opportunities to establish good results.

6 Conclusion

In this paper, we study the problem of exploitation and exploration in mobile context-

aware 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 exper-

imental results demonstrate that our algorithm performs better on average CTR in

various configurations. In the future, we plan to evaluate the scalability of the algo-

rithm on-board a mobile device and investigate other public benchmarks.

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