1

Technical Report: Jointly OptimizingContent Caching and Recommendations

in Small Cell NetworksLivia Elena Chatzieleftheriou, Merkouris Karaliopoulos, Iordanis Koutsopoulos

Department of InformaticsAthens University of Economics and Business, Athens, Greece

Email:{liviachatzi, mkaralio, jordan}@aueb.gr

Abstract—Caching decisions typically seek to cache content that satisfies the maximum possible demand aggregated over all users.Recommendation systems, on the contrary, focus on individual users and recommend to them appealing content in order to elicitfurther content consumption. In our paper, we explore how these, phenomenally conflicting, objectives can be jointly addressed. First,we formulate an optimization problem for the joint caching and recommendation decisions, aiming to maximize the cache hit ratiounder minimal controllable distortion of the inherent user content preferences by the issued recommendations. Then, we prove that theproblem is NP-complete and that its objective function lacks those monotonicity and submodularity properties that would guarantee itsapproximability. Hence, we proceed to introduce a simpler heuristic algorithm that essentially serves as a form of lightweight controlover recommendations so that they are both appealing to end-users and friendly to network resources. Finally, we draw on bothanalysis and simulations with real and synthetic datasets to evaluate the performance of the algorithm. We point out its fundamentalproperties, provide bounds for the achieved cache hit ratio, and study its sensitivity to its own as well as system-level parameters.

Index Terms—content caching, recommender systems, small cells, algorithmic design, wireless networks

F

1 INTRODUCTION

Content caching has been experiencing revived interest inrecent years within the context of current and next gener-ation wireless cellular networks. The soaring demand formobile video services pushes caching functionality towardsthe wireless network edge [2]. Storing popular content atcaches close to the user results in enhanced Quality ofExperience (QoE) for the end users and smaller footprintsof the bandwidth-demanding mobile video traffic within thewireless network.

On the other hand, recommender systems have becomeintegral components of content provision sites. Their mis-sion is to make personalized recommendations for movies,video clips, music songs or other content items that bestmatch the interests and preferences of individual users. This,in turn, improves the users’ satisfaction and boosts theirengagement in the sense that it increases the number ofcontent downloads. For instance, the recommender systemused by Netflix is considered responsible for about 80% ofthe hours streamed at Netflix [3], whereas the Related Videorecommendations generate about 30% of the overall viewson YouTube [4].

Typically, the recommendation engine and the caches atthe wireless network are owned and managed by differententities. Recommender systems are controlled by contentproviders through apps that interact with users, whereas the

Part of this work has been accepted to the proceedings of the IEEE InternationalConference on Computer Communications (INFOCOM), May 1-4, 2017,Atlanta, GA, USA [1]

caching infrastructure is typically possessed and controlledby the wireless network operator. Content providers ofteninsert, through their own or third-party Content DeliveryNetworks (CDNs), servers storing content within other net-works. In the case of cellular networks, these servers tend tobe placed at their egress nodes rather than at their edge.

However, a persistent trend is that players with orig-inally distinct roles in the business value chain, such asaccess network operators and content providers, tend to de-ploy their own content delivery solutions, albeit for differentreasons. Content providers seek to acquire better controlof the network access infrastructure so as to improve theQuality of Experience (QoE) delivered to their subscribers.Netflix Open Connect1 and Google Global Cache2 are twowidely known examples of CDN solutions owned by con-tent providers. Access network operators, on the other hand,primarily seek to minimize costs related to the deliveryof video traffic through external networks. At the sametime, by having storage servers closer to the end- users,telco CDNs can provide their subscribers with faster contentaccess.

In the case of wireless networks, these trends motivatenovel content provisioning scenarios, whereby the coordi-nation of (at least) three different mechanisms is deemedfeasible towards optimizing user- and network-centric per-formance measures. First, content replication at the caches ofdifferent (small) cells can be used to maximize the locally-

1. openconnect.netflix.com/en/2. peering.google.com/

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served demand and optimize the access delays experiencedby users, hence their QoE. At the same time, caching reducesthe traffic at the backhaul links and maximizes the cache hitratio. Secondly, dynamically routing user content requests todifferent cell caches, it can balance the request load acrosscaches, again improving user QoE but also the networkresource usage. Finally, recommender systems can be carefullyused to nudge users towards more network-friendly contentrequest patterns, i.e., they can shape content demand for thebenefit of the caching mechanism.

Motivation: This last mechanism appears to have inter-esting repercussions for the design of caching algorithms.It is, in fact, the coupling between these two mechanisms,content caching and recommender systems, that serves asthe main motivation for this work. Consider, for example,a cell cache serving the users who are associated withthe cell. The rough idea is that the recommender systemdoes not necessarily issue recommendations for contentthat ranks as the top most relevant according to the rec-ommendation algorithm; instead, it could recommend toindividual users cached content that still matches adequatelywith their preferences and, at the same time, attracts strongdemand from many other users. Hence, anticipating thatits recommendations affect the content access patterns ofusers, the recommender system seeks to gently blunt some of theheterogeneity in users’ demands, thus aiming at higher cachingefficiency and better users’ QoE (Fig. 1).

The possibility to dynamically route content requeststhrough different (small) cells within reach of the user addsfurther degrees of freedom to the problem. Besides whichcontent to store, the caching decisions concern where to storeit. Hence, a joint caching and recommendation algorithmcould cache and recommend to a user content items thatrank second, third, or lower in his/her preferences, as longas these items are in great demand in at least one of the cellsthat lie within the coverage of the user. It would insteadavoid caching and recommending an item that, say, ranksfirst in the user interests but is not popular among otherusers in any of the cells the user can associate with.

Our contributions: The main novelty of our work is thatwe take a different viewpoint to recommender systems. Weapproach them as an additional traffic engineering mecha-nism that can also help improve performance measures onthe wireless network side. As a result:

• We define a system model in section 2 that capturesthe coupling between caching decisions and issuedrecommendations. Our viewpoint to recommendersystems raises some concerns, not least ethical ones.Hence, we introduce a measure called preference dis-tortion tolerance, to quantify how much the engi-neered recommendations distort the original usercontent preferences.

• We formulate an optimization problem for the jointtask of caching and recommending content to eachuser in section 3. The objective of the Joint Cachingand Recommendations Problem (JCRP) is to max-imize the cache hit ratio under controlled prefer-ence distortion tolerance. We prove that the JCRPis NP-complete and that its objective function lacksthose monotonicity and submodularity properties

Fig. 1. Illustration of the system model and toy example. Caches areco-located with small cells and serve users with content of their pref-erence. The example shows three users with their content preferencedistributions (2nd column) over six items A-F (1st column). The threeitems (A, C, D) that attract the highest aggregate preference from allusers are locally cached, yielding an expected cache hit ratio of 0.58.Consider a recommender system issuing content recommendations tousers and a naive model for their impact: When an item is recommendedto a user the preference (demand) for that item is boosted by 0.03. Oncontrary, when an item is not recommended to a user, the preference ofthat user for this item decreases by 0.03. When recommendations areissued for the top-3 items in users’ preferences (3rd column), the cachehit ratio drops to 0.55. When recommendations are issued for items thatare both cached and of adequate interest to users, yet not necessarilywithin the top-3 set (4th column), the cache hit ratio increases to 0.67.

that would guarantee its approximability.• We devise a low-complexity practical heuristic algo-

rithm that solves efficiently the JCRP in section 4.The algorithm is essentially a form of lightweightcontrol over user recommendations, so that the rec-ommended content is both appealing to the end-userand more friendly to the caching system and thenetwork resources.

• Finally, in sections 5 and 6, we thoroughly evaluatethe proposed algorithm. The evaluation is carried outboth analytically and through simulations with realand synthetic datasets and establishes main proper-ties and performance bounds of the algorithm. Inthis Technical Report we present a more detaileddiscussion in confront to [5]. More propositions andall the detailed proofs are stated here.

2 SYSTEM MODEL

2.1 Caches, content, users

Our model involves a set of caches C, a catalogue of contentitems (e.g., video clips), I , and a set of users, U (Figure 1).

2.1.1 Caches

Caches are co-located with wireless network microcells thattypically have a range in the order of a few hundred meters.Each cache z ∈ C has limited storage, Cz , which is measuredin normalized file size units. At any point in time, it stores afinite set of files, referred to as the cache placement Pz . Anadditional cache is installed on a backend server, e.g., in thecloud. This “cache” is assumed to have enough capacity tostore copies of the entire catalogue.

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TABLE 1Notation table

Notation ContextCz Storage capacity of cache zM Number of thematic categoriesLi Normalized length of item i

f i(j) Feature vector value of content item i in feature jfu(j) Feature vector value of user u in feature j

pprefu Inherent content preference distribution of user uaui Similarity of user u and item iprecu Probability distribution due to recommendationprequ Content item request probability distribution of user u

(recommended items)prequ Content item request probability distribution of user u

(non-recommended items)R Number of recommended itemsWu Recommendation window of user uKu Length of Wu

rd Preference distortion toleranceHs Cache hit ratio under scheme s

RCinu Provisional set of recommended items to u

P Cache placementRCf

u Final set of recommended items to uZD Zero-distortion schemeUD Unbounded-distortion scheme

CawR Caching-aware recommendations scheme

2.1.2 ContentContent items are relevant to one or more of a set ofM thematic categories. The detail and resolution of thiscategorical separation may vary (e.g., “soccer” might bea distinct category, but it may also be further split intoEnglish/French/Spanish soccer). Such information may bestored in content metadata in the form of (hierarchical) tags.

The M thematic categories serve as the feature set thatdescribes items. Namely, each item i ∈ I of finite normal-ized size Li is represented by a feature vector f i, whose jth

element f i(j), j ∈ [1, ..,M ] denotes the score of item i infeature j, i.e., how relevant is item i to thematic categoryj. These relevance scores assume values in [0,1] and arenormalized so that

∑Mj=1 f

i(j) = 1, ∀i ∈ I . Replicas ofeach content item may be stored in any set of the small cellcaches, besides the backend cache, depending on the actualcaching decisions.

2.1.3 UsersAt any point in time, each user u ∈ U is located withinrange of a different subset of the network (micro)cells.Theoretically, the user might access different content itemsthrough different caches, each time dynamically changinghis/her association depending on the requested content3.In this paper, we assume that users do not change theirassociation point in the network dynamically in response tocontent requests. Users are rather statically associated withcertain cells, depending on the quality of radio signals andthe load of the radio network, in line with user associationpractices in current wireless networks. A direct consequenceof this assumption is that the caching decisions are madeindependently in each cache-enabled small cell.

Users are described by similar feature vectors fu ∈[0, 1]M as the content items. Each vector element fu(j), j ∈

3. The combination of caching with dynamic user associations andcontent routing has been investigated in literature, e.g., see [6].

[1, ..,M ] expresses how much user u is interested in contentclassified under thematic category j. We normalize thesevalues as well, i.e.,

∑Mj=1 fu(j) = 1, ∀u ∈ U .

Practically, content provision sites draw on the historyof users’ content downloads, and more broadly their inter-actions with the site, to infer these vectors. We elaborate onthis in section 6.1.

2.2 Content preferences of users

The demand for content items is time-varying. It growsfor some finite time after the content item first becomesavailable for download, and then it gradually fades out [7],[8]. Our work concerns time scales over which the demandfor each item can be considered “fixed”, in the order of afew hours within a day [9], [10]. Namely, content demandpredictions and caching decisions are made once every suchan interval, and user content request patterns change slowlyover that interval.

On the user side, we distinguish between inherent con-tent preferences of users and the eventually issued contentrequests by them. Hence, each user u can be describedby a content preference distribution, pprefu (i), i ∈ I , with∑i∈I

pprefu (i) = 1, which captures his/her original prefer-

ences over all items. The preference of user u for item i,pprefu (i), can be inferred from the feature vectors fu and f i.In this paper, we use for this purpose the cosine similarityindex, aui, of vectors fu and f i [11]4, defined as

aui =

M∑j=1

fu(j) · f i(j)√√√√ M∑j=1

fu(j)

√√√√ M∑j=1

f i(j)

.

Normalizing these index values over all items yields thecontent preference distribution pprefu

pprefu (i) =aui∑

i∈Iaui

. (1)

However, the content that users eventually request alsodepends on the recommendations issued to them, so thatthe probability with which user u requests item i, prequ (i),differs from pprefu (i). We describe our modeling approachto the recommendations’ impact in the next paragraph.

2.3 The impact of recommendations on user contentrequests

The system recommendations affect the relative user de-mand for all content items. In principle, they boost thedemand for the recommended items and at the same timeproportionately decrease the demand for remaining items. Itis less clear how recommender systems quantitatively mod-ulate the a priori preferences of a user pprefu so as to yieldthe ultimate content request distribution prequ . Modeling inliterature tends to be both intuition- and evidence-driven.

4. Measures of similarity between distributions such as the Pro-portional Similarity, the Kullback-Leibler distance and the Hellingercoefficient could also be used in this respect [12]

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Fig. 2. Impact of recommendations on user requests. The content itemsare ranked in decreasing order of user preference and only items withinthe recommendation window are recommended. A priori content pref-erence distribution for arbitrary user u, its recommendation window Wu

of size Ku (black), and the resulting content request probability afterrecommendations (red).

In [13], for example, the recommendations are mapped toa new distribution precu over the content items and prequ (i)is taken to be equal to max{pprefu (i), precu (i)}. On the otherhand, there is strong experimental evidence that both thenumber of recommended items and their order within therecommendation list have a high impact on the a posterioridistribution of the users’ demand. For instance, the ”RelatedVideo” recommendation lists of YouTube is shown to be themain source of requests for its content, since items rankedhigher up in a list of recommended items attract moreuser interest than items at lower positions. (e.g., [4], [14]).This finding is more relevant for users that access contentthrough small form-factor devices such as mobile phones,in which case it is less convenient to scroll down the wholerecommendation list.

Hence, in modeling the impact of recommendations, wemake two assumptions:

Assumption 2.1. The impact of a recommendation for item ion the demand that is eventually expressed by a user u for thisitem is a non-increasing function f(.) of both item’s i position inthe recommendation list, rnkLu (i) ∈ [1, R], and the number ofrecommended items, R.

In section 6.1 we consider specific instances of precu thatsatisfy this assumption.

Assumption 2.2. The content request distribution is a convexcombination of the two distributions, pprefu and precu and is givenby

prequ (i) = wru · precu (i) + (1− wr

u) · pprefu (i) (2)

for each of the R items that are recommended to u, and by

prequ (i) = (1− wru) · pprefu (i) (3)

for each one of the (|I|−R) items not recommended to user u. Therecommendation weights wr

u in (2) and (3) express the importanceuser u attaches to recommendations.

Equations (2) and (3) capture the way recommendationsshape content requests that are ultimately issued by useru. The request probabilities are boosted when compared tothe initial ones for recommended items, and they decreasefor non-recommended ones, so that the resulting contentrequest distribution remains a probability distribution (seeFig. 2).

2.4 Engineering the user recommendationsThis capability of recommender systems to shape user de-mand for content renders them a powerful tool for contentdemand shaping. This way, recommender systems couldbe actively used to optimize network-centric performanceobjectives, in what marks a departure from their nominaluser-oriented mission. Our approach to this is summarizedin Fig. 2 and described in what follows.

Assume that the recommender system seeks to recom-mend R new items to each user u, where R may range from1 up to a few (e.g., 5-10) items. Instead of issuing recom-mendations for the top R items in u’s content preferencedistribution pprefu , the system selects R items among theones residing within a recommendation window Wu that isdefined by the top Ku items, where Ku > R, as shown inFig. 2. Namely, the recommender system artificially inflatesthe set of candidate items for recommendation for each useru by a user-specific factor Ku/R. When doing so, the systempreserves two properties addressing the ethical concernsdescribed in section 1 regarding the manipulation of rec-ommendations:

• It preserves the rank of recommended items in the originaluser content preferences. If an item i is recommendedat higher rank than item j, it holds necessarily thatpprefu (i) ≥ pprefu (j).

• It controllably bounds the distortion that its recommenda-tions introduce to the original user content preferences.

In the worst case, the system will end up recommendingitems that are ranked in positions {Ku − R + 1,Ku −R + 2, . . . ,Ku} in decreasing order of user content pref-erences (ref. Fig. 2), instead of the items in top-R positions{1, 2, . . . R}. We define the worst-case user preference distor-tion measure, ∆u to be

∆u(Ku, R) = 1−

∑j:rnku(j)∈

[Ku−R+1,Ku]

pprefu (j)

∑j:rnku(j)∈[1,R]

pprefu (j). (4)

where rnku(i), i ∈ I , is the rank of item i in user’s u contentpreferences.

The denominator in (4) equals to the total request prob-ability of user u for the top R items, which are the onesa typical recommender system would recommend. Thenumerator, on the other hand, equals to the total requestprobability of user u for the bottom R items in the recom-mendation window. Hence, ∆u(Ku, R) expresses the worst-case deviation from initial user request probabilities, thatmay result from the choices of our scheme when comparedto a typical ”honest” recommender system. As such, thismetric is admittedly conservative and it denotes an upperbound on the possible distortion of original user requestprobabilities.

The size of the recommendation window, Ku, introducesan interesting tradeoff. Higher Ku values allow for moreflexibility in selecting items to recommend to users andshaping their demand in favor of caching efficiency, as itwill be seen in the sequel. But at the same time, a higher Ku

value may result in higher distortion of user preferences, ascan be readily seen in (4).

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3 THE JOINT CACHING AND RECOMMENDATIONSPROBLEM

The net outcome of these recommendations is that a givencache placement {Pz : z ∈ C}, may satisfy a portion of thetotal demand in the cell, as measured by the cache hit ratio5

H =

∑u∈U

∑i∈P

prequ (i)∑u∈U

∑i∈I

prequ (i). (5)

On the user side, the requirement is to maximize thenumber of requests that can be satisfied by the cell cache(cache hits). This results in lower content access delays andhigher user QoE. At the same time, since fewer requestshave to be satisfied by the backend server, the utilization ofbackhaul links is lower. In other words, the maximization ofthe cache hit ratio serves both types of requirements.

Formally, let {yi} and {xui}, i ∈ I, u ∈ U be two setsof binary decision variables with yi = 1 when item i iscached and yi = 0, otherwise; and xui = 1 when item iis recommended to user u and xui = 0 when it is not. Theobjective of the joint caching and recommendation decisionsare then to

maxy,x

∑u∈U

∑i∈Wu

yi(xuiprequ (i) + (1− xui)prequ (i)) (6)

s.t.∑i∈I

yiLi ≤ C (7)∑i∈Wu

xui = R ∀u ∈ U (8)

yi, xui ∈ {0, 1} u ∈ U , i ∈ Wu. (9)

In (6) and (8),Wu denotes items within the recommendationwindow of user u. The cardinality of this set is

Ku = max{k|∆u(k,R) ≤ rd(u)}, (10)

where rd(u) ∈ [0, 1) denotes the user-specific preferencedistortion tolerance, an upper bound on user preference dis-tortion in (4) that should not be exceeded for any user. Ourformulation implies that the system could provide userswith the opportunity to determine themselves how muchdistortion tolerance they are willing to tolerate. Inequality(7) reflects the cache storage capacity constraint, whereasinequalities (8) ensure that no more than R items are recom-mended to every user.

3.1 Problem complexity and approximability propertiesWe refer to the problem (6)-(9) as the Joint Caching andRecommendations Problem (JCRP).

Proposition 3.1. The Joint Caching and Recommendations Prob-lem is NP-complete.

Proof. We work with the decision problem variant of JCRP,to which we refer as the Joint Caching and RecommendationDecision Problem (JCRDP).

JCRDecisionProblem: Consider a set of users U , acatalogue I of content items with lengths Li, i ∈ I , user

5. Since the caching decisions are made independently for each cache(ref. 2.1.3), we drop the index z from subsequent references to cacheplacements, i.e., we write P instead of Pz

demand distributions pprefu and recommendation windowsetsWu, u ∈ U , a cache capacityC and a real numberQ > 0.Given (7)-(9) and semantics of {yi}, {xui} as in the JCRP ,are there are a cache placement and item recommendationsto each user so that∑

u∈U

∑i∈Wu

yi(xuiprequ (i) + (1− xui)prequ (i)) ≥ Q, (11)

where prequ (i) and prequ (i)) are given by equations (2) and(3)?

Let a JCRDP instance be denoted asJCRDP (U , I, ppref ,W, R, C, L,Q). It is easy to seethat, given a cache placement and lists of recommendationsfor each user, we can check in polynomial time whether theysatisfy or not (7)-(8) and (11). Hence, the JCRDP lies inNP . We prove that it is NP-complete by generalization, byshowing that the 0-1 Knapsack Problem (0-1 KSP ) reducesto a special case of the JCRDP , i.e., 0-1 KSP ≤P JCRDP .

Consider an instance of JCRDP with such preferencedistributions of users that their recommendation windowsare of size R. Then, the recommendations are trivially fixedfor each user; namely, xui = 1 for each item i that ranks inthe first R positions in the individual preference distribu-tions and xui = 0 otherwise. The JCRDP now simplifiesto asking whether there are {yi} variables so that:∑

u∈Uyivi > Q (12)

s.t.∑i∈I

yiLi ≤ C (13)

yi ∈ {0, 1} i ∈ I, (14)

where vi is given by

vi =∑u∈U

xuiprequ (i) + (1− xui)prequ (i)).

Equations (12)-(14) constitute the decision version of the 0-1KSP , where l and v are the sizes and values, respectively,of the items that have to be packed within space C .

Moreover, assuming an oracle that solves JCRDP , re-turning the recommendations lists for all users and thecache placement, we can directly solve the decision versionof the 0-1 KSP . Conversely, given the solution to the 0-1KSP , we get the caching policy for the special case of theproblem, where the recommendations are trivially obtained.

As a first step towards an efficient approximation algo-rithm, we investigate the monotonicity and submodularityof the JCRP (JCRDP ) objective function. We recall therelevant definitions in what follows. Let S be a finite setof elements (interchangeably called universe or ground set)and X , Y any two subsets of S satisfying X ⊆ Y ⊆ S.A set function f : 2S → R is called monotone if f(X) ≤f(Y ),∀X,Y ⊆ S. Moreover, f is called submodular, if forany element e ∈ S \ Y , it holds that fX(e) ≥ fY (e), wherefA(e) = f(A∪e)−f(A). Namely, the extra marginal benefitfrom adding an item to a set decreases as this set growslarger. Similarly, f is called supermodular, if for any elemente ∈ S \ Y , it holds that fX(e) ≤ fY (e).

We now claim that:

6

Proposition 3.2. The objective function of the JCRP is nonmonotone.

Proof. The objective function in (6) corresponds to the non-normalized expected cache hit ratio of the JCRP . Eachcontent item i that is a candidate to be cached carries non-negative utility

v(i) =∑u∈U

prequ (i) (15)

=∑u∈U

(1− wru)pprefu (i) +

∑u:i∈Wu

wrup

recu (i).

The first summand captures the original demand for theitem and the second one the added value the item acquiresdue to recommendations made to users for it.

The objective function is monotone if it increases or, inthe worst case, remains constant, every time a new itemis added to the cache (yi changes from 0 to 1) or to therecommendation list of any user (xui changes from 0 to 1).

Monotonicity with respect to yi: Consider that we add itemi to the cache, that is yi=1. Then the cache hit ratio willincrease by a factor∑

u∈U(1− wr

u)pprefu (i) +∑

u:xui=1

wrup

recu (i)

and the system will have a positive gain.Monotonicity with respect to xui: Now consider the case

where an item i is inserted in the recommendation list ofuser u, i.e., xui(i) = 1. When this happens, the followingscenarios are possible with respect to its impact on a specificuser and the cache placement:

(c1) Item i is cached (yi=1).(c2) Item i is not cached (yi=0) and is recommended at a

lower rank than any other cached item in the recommenda-tion list of user u.

(c3) Item i is not cached (yi=0) and seizes the positionof a cached item, say j with yj=1, in the recommendationlist of u (item j, and possibly other items, move to lowerpositions in this list).

In cases (c1) and (c2) the contribution of item i to thecache hit rate is positive and zero, respectively. On thecontrary, in (c3), the contribution of i is negative since itreduces the value of the cached item j, as well as that ofany other items that shift to lower-rank positions in therecommendation list of u (recall assumption 2.1). Thus, theobjective function in (6) is non monotone.

Proposition 3.3. The objective function of the JCRP is neithersubmodular nor supermodular.

Proof. The objective function would be submodular (resp.supermodular) if it exhibited consistently decreasing (resp.increasing) returns as new items are added to the cache orthe recommendation list of any user.

Consider sets X,Y to be two sets of cached items withX ⊆ Y . When a new item i ∈ I \ Y is added to the cache(yi=1), the gain in cache hit ratio is positive and fixed (referto (16)).

When a new item i is recommended to user u, i.e., xui =1, the following cases are possible:

(c1) Item i is cached neither in X nor in Y .

(c2) Item i is cached in both X and Y .(c3) Item i is cached in Y but not in X .In (c1), the marginal gain in cache hit ratio is zero for

both sets X and Y .In (c2), the marginal gain in cache hit ratio exhibits

diminishing returns and the objective function behaves asa submodular one. More specifically, if ku cached items arealready in the recommendation list of user u, the addedvalue wr

uprecu (i) that i generates for the cache hit ratio is

that of a recommendation in the position ku+1 in the list.But ku can only increase for every user as the cache growsand the impact of a recommendation for i is a decreasingfunction of its rank in the list (ref. assumption 2.1).

In (c3), the marginal gain in cache hit ratio increases withenlarged cache placements. Marginal gain is achieved onlyfor set Y . For X , the cache hit ratio does not change (if thereare no cached items following item i in the recommendationlist of u) or even decreases (if i precedes one or more cacheditems in the recommendation list of u), as in case (c3) inproposition 3.2. Thus, the objective function behaves as asupermodular one.

Overall, the objective function is neither submodular norsupermodular with respect to variables xui.

Summarizing propositions 3.2 and 3.3, the objectivefunction is neither monotone nor submodular. Hence, moregeneral techniques that yield approximability guarantees forthis category of functions, e.g., [15], [16], and have been oftenapplied in caching problems e.g., [17], [18], are not applicableto the JCRP .

In the following section, we propose an efficient heuristicalgorithm for solving the JCRP. Although the algorithmdoes not lend to rigorous approximability analysis (ref.section 4.2), it is computationally simple (ref. section 4.1)and exhibits excellent performance (ref. section 6).

4 AN ALGORITHM FOR THE JOINT CACHING ANDRECOMMENDATION PROBLEM

4.1 Description of the algorithmOur Caching-aware Recommendations (CawR) algorithmproceeds in three steps, as shown in Fig. 3 and it is sum-marized in the pseudocode of Algorithm 1.

The first step is an initialization step where a provisionalset of recommended items RCinu is derived for each user.Input to this step are the content preference probabilitydistributions of users. Recommendations are made for thetop-R items in the user preferences but, contrary to whatwould happen with a typical recommender system, theserecommendations are not communicated to the user; theyare only relevant as intermediate result of the algorithm’soperation.

The second step is a content placement step, where wedetermine which content should be cached. To this end, wecompute the content request probabilities according to (2),(3). All content items are assigned utilities that equal theaggregate request probability they attract:

v(i) =∑u∈U

prequ (i) i ∈ I. (16)

The optimal placement is then an instance of the 0-1 KSP.We use the Dynamic Programming (DP) FPTAS algorithm

7

Fig. 3. Schematic outline of the three-step algorithm for the joint caching and recommendation problem.

in ([19], §8.2) to obtain an (1-ε), ε > 0 approximation of theoptimal solution; let P denote this placement.

Finally, in the recommendation amendment step, the origi-nal recommendations to users are amended so as to max-imize the utility (i.e., expected attracted requests) of thecached content. To this end, we first identify for each useru the set of Ku items in his/her recommendation windowfrom (10). Then we compare the item sets P and RCinu . Twopossibilities exist:

• If RCinu ⊆ P , then the original recommendationsderived in the initialization step remain intact (andthe resulting user preference distortion is zero).

• If |RCinu⋂P| = F1 ∈ [0, R − 1], then the F1

items that appear in both sets are retained in thefinal recommendation list; F = min{R − F1, F2}F2 = |(Wu \ RCin

u )⋂P|, most preferred cached

items appearing in the recommendation window ofu (but not in the recommendation set derived in theinitialization step), are added to the recommendationlist for u, replacing the bottom-F items inRCinu ; and,if there is still space (F1 + F < R), the remainingrecommendations are made for the (R − F1 − F )least popular items out of the (R − F1) remaining(non-cached) items in RCinu .

The final set,RCfu, of R items that are recommended to useru are in general different from the equal-size provisionalset RCinu derived in the initialization step. Since the val-ues of prequ after the recommendation amendment step aredifferent, one might think that the algorithm returns to thecontent placement step and runs another round of steps 2and 3. In Proposition 4.1 we prove that this is not the case,and that our algorithm terminates in a single round.

Proposition 4.1. CawR terminates after a single execution of therecommendation amendment step.

Proof. It suffices to show that the recommendation amend-ment step does not motivate any change in the cachedcontent. Such a change would occur if the modification ofrecommendations resulted in change of item utilities (see(16)) so that

∃ j ∈ P, j′ /∈ P : v(j′) > v(j). (17)

However, the recommendation amendment step increasesthe utility of an item already in the cache, when issuingrecommendations for it to additional users than those in theinitialization step; or, in the worst-case, it leaves it intact.At the same time, it reduces or leaves intact the utility ofitems that have not been included in P during the content

placement step. Hence, condition (17) cannot be fulfilled andthe cache placement P does not change.

Hence, the algorithm essentially sets the cache placementon the basis of the original recommendations to users (withzero user preference distortion). Then, it selectively changesrecommendations to nudge individual user preferences to-wards content that attracts demand from the overall userpopulation. This way, the utility of the cached content, i.e.,the demand it attracts, grows and the expected cache hitratio increases.

In the toy example of Fig. 1, CawR first sets the provi-sional recommendation list RCin

u to the R most preferreditems for every user, as highlighted in the 2nd column.The resulting demand distributions are shown in the 3rdcolumn. These recommendations are not shown to the end-users. In the second step, CawR computes the utility ofeach item from Eq. (16) and caches items A,C,D. In the finalstep, CawR compares the recommendation window Wu ofeach user u with {A,C,D} and determines the final listsof recommendations RCfu, which are issued to the users.In our case, Wu1 = {A,B,C,D}, Wu2 = {A,C,D,E, F},andWu3 = {A,B,C,D,E}, respectively. The sets RCfu arethose highlighted in the 4th column in Fig. 1.

4.2 Complexity of the CawR algorithm

The manipulation of recommendations injects controllabledistortion to the original user content preferences. In theworst case, the algorithm recommends to user u the bottomR of the top-Ku items, resulting in at most ∆u distortionof the recommendations an “honest” recommender systemwould make.

In the first step, our algorithm sorts the list of the itemsand finds the most preferred ones for each user at timeO(|U| · |I| · log |I| + |U| · |I|) = O(|U| · |I| · log |I|). In thesecond step the algorithm computes a utility for every itemand then uses the DP FPTAS algorithm for the 0-1 KSP. Thisimplies a complexity of O(|I|+ |I| · |C|) = O(|I|2) since thecache capacity is upper bounded by the total catalogue size.In the third step, the algorithm compares the items withinthe recommendation window of each user against the cacheplacement to define the final recommendations, leading toO(|U| ·maxu(|Wu|) · |C|). Since the size of the recommenda-tion window is naturally bounded by the catalogue size, thetotal computational complexity of CawR is O(|U| · |I|2).

In the two sections that follow, we draw on both analysis(5) and simulations with real and synthetic datasets (6)to gain further insight to the properties of the proposedalgorithm.

8

Algorithm 1 The CawR algorithm

Input: Probabilities pprefu , weights wru, recommendation

windowsWu, ∀u ∈ U , number of recommendations ROutput: Content placement P and recommended item setsRCfu,∀u ∈ U .Step 1:

1: Set the initial recommendation list RCinu to the R mostpreferred items of the user and prec to f(rnkLu (i), R)(ref. Assumption 2.1).

2: for every user u ∈ U and item i ∈ I do3: Compute the content request probabilities prequ (i)

from (2) and (3).4: end for

Step 2:5: for every item i ∈ I do6: Compute its utility from (16).7: end for8: Use the DP (1 − ε)-approximation algorithm, ε > 0, to

solve the 0-1 KSP and derive the content placement P .Step 3:

9: for every user u do10: Add items in RCinu

⋂P to the final recommendation

list RCfu for u.11: if RCfu is not full then12: Add to set RCfu items that are both cached and

withinWu in decreasing order of preference proba-bility till it is filled up.

13: end if14: if RCfu is still not full then15: Add to the list items out of the remaining ones in

RCinu in decreasing order of preference probabilitytill the set is filled with R recommended items.

16: end if17: end for

5 PROPERTIES AND PERFORMANCE BOUNDS OFOUR ALGORITHM

In this section, we compare the performance of our algo-rithm to benchmark recommender schemes and analyze itssensitivity to the maximum distortion tolerance parame-ters, {rd(u)} and the user content preference distributions,{pprefu }. We codify our results as propositions.

5.1 Benchmark recommender schemesWe consider three alternative schemes for determiningwhich content to cache and which to recommend to eachuser. They serve as plausible comparison references for ouralgorithm and help set bounds for its performance.

Zero-distortion (ZD) scheme. The scheme recommendsto each user the top-R items in his/her preferences andcaches the C items attracting the highest aggregate demand,after accounting for the impact of recommendations. Hence,the recommendations follow precisely the user preferences,in line with what recommender systems nominally do, andthe cache placement adapts to them.

Unbounded-distortion (UD) scheme. This scheme ranksitems in order of decreasing aggregate demand over allusers, after taking into account the factors (1 − wr

u) thatweigh users’ original preferences. It then caches the top-C

of those and recommends to all users the same top-R items.Contrary to the ZD scheme, it is now the cache placementthat determines the individual recommendations, cateringfor no bounds on the resulting distortion of the inherentuser preferences.

Proposition 5.1. When recommendations follow assumptions 2.1and 2.2 and the user preference distortion tolerances are relaxed,i.e., Wu ≡ I ∀u ∈ U in (6) and (8), the UD scheme is theoptimal solution to the JCRP.

Proof. Let P be the cache placement under the UD scheme.From the definition of UD, it holds that∑u∈U

∑i∈P

(1− wru)pprefu (i) ≥

∑u∈U

∑j∈P′

(1− wru)pprefu (j) (18)

for any other placement P ′, which may result from anyother algorithm alg solving the JCRP.

Moreover, by recommending only cached items, the UDscheme captures as much as possible from the potentialimpact of the recommendations on each user, i.e., :∑

i∈(RCUDu ∩P)

precu (i) = 1 ≥∑

j∈(RCalgu ∩P′)

precu (j) (19)

where RCUDu and RCalgu are the recommendation lists for

user u under the UD and alg schemes, respectively. Weigh-ing (19) by wr

u in both parts, summing the weighed termsover all users u ∈ U and adding by parts to inequality (18),we get ∑

u∈U

∑i∈P

prequ (i) ≥∑u∈U

∑i∈P′

prequ (i) (20)

Dividing both parts by∑u∈U

∑i∈I

prequ (i) = |U|, we derive

HUD > Halg (21)

for the cache hit ratios achieved by the UD scheme andevery other scheme alg solving the JCRP under relaxed userpreference distortion tolerances.

Least Frequently Used (LFU) caching algorithm. Thealgorithm caches items that attract the maximum aggregatedemand over all users, but it does not recommend anythingto them. It is known that LFU maximizes the cache hit ratiofor a single cache in the absence of recommendations.

Denoting the expected cache hit ratio each schemeachieves by Hs, s ∈ {ZD,UD,CawR}, we can show that

Proposition 5.2. The expected cache hit ratios achieved by thethree schemes that issue recommendations satisfy:

HZD ≤ HCawR ≤ HUD. (22)

Proof. Let us define by hu,s(i) the part of the experiencedcache hit ratio that is due to the preference of user u foritem i under scheme s and the cache placement it induces:

hu,s(i) =

{prequ,s (i) if i is cached0 otherwise

CawR vs. ZD Our algorithm and the ZD algorithmdifferentiate in the recommendation amendment step (ref.Fig. 3). In that step, CawR may change the recommendationsthat the nominal recommendation scheme (ZD) would issue

9

to the end users. This happens every time at least one of theR items ranking top at the preferences of u, say item m,is not part of the cache placement and there is at least onecached item, say n, that is part of the u’s recommendationwindow. CawR then will issue a recommendation for ninstead of m since

hu,CawR(m) = 0 ≤ hu,CawR(n) (23)

It then holds:

hu,ZD(m) = 0 = hu,CawR(m) andhu,ZD(n) = (1− wr

u) · pprefu (n) (24)

≤ wru · precu (n) + (1− wr

u) · pprefu (n) = hu,CawR(n)

namely, the replaced item m does not add anything tothe cache hit ratio under both schemes, whereas the con-tribution of the item n is boosted under CawR with therecommendation part.

For any other item p in the cache placement, recom-mended either by both schemes or by neither of them, itholds

hu,CawR(p) = hu,ZD(p) (25)

If we denote by Im(u), In(u), and Ip(u), the resultingsubsets of items for user u, with

|Im(u)|+ |Ip(u)| = |In(u)|+ |Ip(u)| = |P| ∀u ∈ U (26)

and sum their marginal contributions to the cache hit ratio tocompute the aggregate contribution of user u, h(u, s), underthe two schemes, we get

h(u,CawR) =∑

i∈Ip(u)

hu,CawR(i) +∑

i∈In(u)

hu,CawR(i)

≥∑

i∈Ip(u)

hu,ZD(i) = h(u, ZD) (27)

the equality being relevant when Ip(u) = I (or, equiva-lently, Im(u) = In(u) = ∅).

Summing over the user population and dividing by thedenominator in (5) we get

HCawR =∑u∈U

h(u,CawR) ≥∑u∈U

h(u, ZD) = HZD (28)

CawR vs. UD: From Proposition 5.1, the scheme UD isoptimal in terms of cache hit ratio for the JCRP when theconstraints about the tolerable distortion of user preferencesare relaxed. Hence, the cache hit ratio under the UD schemesets an upper bound to the cache hit ratio under the op-timal algorithm (OPT) for the JCRP (without relaxing thedistortion constraint), and, eventually, for the cache hit ratioachieved by the CawR algorithm. Namely

HCawR ≤ HOPT ≤ HUD (29)

Thus, the performance of the unbounded- and zero-distortion schemes set an upper and a lower bound, respec-tively, for what is achievable with CawR.

It is less intuitive how LFU compares with the threeschemes issuing recommendations since they weigh theinherent user content preferences with factors (1 − wr

u) to

determine the cache placement. We explore these compara-tive relationships as well as the tightness of the bounds in(22) with numerical simulations in section 6.

It is also quite straightforward to show that:

Proposition 5.3. The expected cache hit ratio under the un-bounded distortion scheme is the same irrespective of how manyand which items out of the C cached ones are recommended.

Proof. Let PUDR be the set of the top R cached items with

the highest aggregate demand. These items will be recom-mended to all users in the UD scheme. The expected cachehit ratio under UD equals:

HUD =

∑u∈U

∑i∈P

prequ (i)∑u∈U

∑i∈I

prequ (i)

=

∑u∈U

(1− wru)

∑i∈P

pprefu (i) +∑u∈U

wru

∑i∈PUD

R

precu (i)

∑u∈U

(1− wru)

∑i∈I

pprefu (i) +∑u∈U

wru

∑i∈I

precu (i)

=

∑u∈U

(1− wru)

∑i∈P

pprefu (i) +∑u∈U

wru∑

u∈U(1− wr

u)∑i∈I

pprefu (i) +∑u∈U

wru

(30)

=

∑u∈U

(1− wru)

∑i∈P

pprefu (i) +∑u∈U

wru

|U|(31) suggests that the expected cache hit ratio does notdepend neither on the actual set of recommended items,RUD

u , nor on its cardinality.

Therefore, the additional demand boost that recommen-dations can generate for cached items and a given setof users is invariable under the UD scheme. The actualrecommendation choices only affect the way this demandboost is spread across different cached items but not thetotal cache hit ratio.

Our algorithm exhibits, under conditions, similar insen-sitivity properties to the recommendation set.

Proposition 5.4. Whenever the recommendation window Wu ofuser u includes more than R cached items, his/her contribution tothe expected cache hit ratio under CawR is the same irrespectiveof which R cached items are recommended to the user.

Proof. From (2) and (3), the portion of requests from user uthat can be satisfied is∑

i∈RCfu

prequ (i) +∑

i∈P\RCfu

prequ (i) (31)

= wru

∑i∈RCf

u

precu (i) + (1− wru)

∑i∈P

pprefu (i)

When |Wu ∩ P| ≥ R, RCfu ⊆ P and the recom-

mendations can be fully directed to cached items so that∑i∈RCf

u

precu (i) = 1 and (31) is rendered independent of the

actually recommended cached items.

If the number of cached items in the recommendationwindow Wu is less than or equal to R, then CawR rec-ommends these items as first in the list and appends theremaining items (it does not matter which ones, since they

10

do not contribute to the cache hit ratio). Contrary to the un-bounded distortion scheme, the cache hit ratio under CawRis sensitive to the number of recommended items sincerecommendations are also directed to non-cached items.

5.2 Sensitivity analysis to parameters of CawR5.2.1 Monotonicity and submodularity of HCawR with re-spect to the distortion tolerance parametersBy definition, the performance of the zero- and unboundeddistortion schemes is not dependent on the value of thedistortion parameter, rd. The parameters {rd(u)}, u ∈ Uin CawR control the amount of distortion that is toleratedwith respect to the original user content preferences. Higherrd(u) values imply larger Wu sizes, as can be seen from (4),and higher chances to find cached items in them. This isinterpreted into higher cache hit ratio when at least one ofthe currently issued recommendations is for a non-cacheditem. In that case, CawR can replace its recommendation(s)for one (or more) of these items with recommendations forone (or more) of the cached items that are included in theenlarged Wu.

Proposition 5.5. HCawR is a monotonically increasing functionof the distortion tolerance parameters {rd(u), u ∈ U}.

Proof. By definition of the recommendation window, it is

rd ≤ r′d ⇔Wu ≤ W ′uNaturally,

Wu ≤ W ′u ⇔ |Wu ∩ P| ≤ |W ′u ∩ P|

From step 3 of CawR,

|Wu ∩ P| ≤ |W ′u ∩ P| ⇔ HCD(rd) ≤ HCD(rd′),

which completes the proof.

Less strict claims can be made about the submodularityof HCawR with the {rd(u)} parameters.

Discussion: The increase of rd results in larger (or, in theworst case, of the same sizes) recommendation windowsWu

so that more items can be recommended to each user. Onthe other hand, as the window grows, the number of userswho are recommended items not in cache drops. That is, theadditional benefit from a marginal increase of the windowis smaller.

Let rd,1 and rd,2 be two values of the distortion toleranceparameter, with rd,1 < rd,2, and Wu,1 ≤ Wu,2 the rec-ommendation windows corresponding to them. Note thatas content placement in step 2 of CawR is based on the“honest” recommendations, the portion of pprefu satisfiedby the cached items will be the same. Thus, because of (2)and (3), and since the cache capacity is fixed, changes inthe expected cache hit ratio are due to the precu factors. Thehit ratio gain ∆H due to an increase of rd,1 by ∆rd (andincrease of the recommendation window by ∆Wu,1 ≥ 0) is

∆H1 =∑

u:|Wu,1∩P|<R

∑m∈(P∩∆Wu,1)

wrup

recu (m) (32)

whereas an increase of rd,2 yields gain

∆H2 =∑

u:|Wu,2∩P|<R

∑m∈(P∩∆Wu,2)

wrup

recu (m) (33)

Strictly speaking, it may hold ∆Wu,1 < ∆Wu,2, dependingon the pprefu distribution of the user. Namely, an increase∆rd(u) may add more items to his/her recommendationwindow at higher rd(u) values. But since items are cachedbased on the aggregate demand probabilities over all users,the top items in the cache placement are also expected tobe occupying higher-rank positions in the recommendationwindows of the majority of the users. Thus, it is expectedthat items in the top positions of the recommendation win-dows contribute more to the cache hit ratio than those in thelower positions. Combining the above, we conjecture that forrecommendation windows Wu,1 < Wu,2 with increments∆Wu,1 and ∆Wu,2 respectively, it holds ∆H1 ≥ ∆H2.Moreover, items are recommended only if they are in therecommendation window of the users.

5.2.2 Sensitivity of HCawR to the individual user contentpreferencesAlthough the exact values of HCawR and HZD may varywidely depending on the user content preference distribu-tions, {pprefu , u ∈ U}, we can state that:

Proposition 5.6. As the individual content preference distribu-tions become more skewed, HZD and HCawR tend to convergewith each other.

The key remark is that as the distributions {pprefu }become more skewed, the recommendation windows be-come smaller. Therefore, the additional flexibility of CawRin selecting items to recommend tends to vanish and itsrecommendations to the users coincide with those of the ZDscheme. In fact, the recommendations of the two schemesexactly coincide when Ku = R.

6 EXPERIMENTAL EVALUATION OF OUR ALGO-RITHM

6.1 Datasets and default parameter settingsWe use both synthetic and real datasets [20] to derive theuser and item feature vectors, fu u ∈ U and f i i ∈ I ,respectively, and then infer the user content preferencedistributions pprefu (see section 2). The purpose of using realdatasets is three-fold: a) to show how our model of userpreferences and content items can be informed by real data;b) to drive a more “realistic” evaluation of the cache hitratio CawR achieves; and (while doing so) c) to validate thetheoretical claims made in section 5. With synthetic datasets,on the other hand, we can control the experimentationsettings and analyze the sensitivity of our algorithm toimportant variables such as the (dis)similarity of contentpreferences across users. Experiments were performed withthe Movielens dataset as well as with synthetic datasets.

6.1.1 MovieLens datasetThe analyzed dataset is a subset of the MovieLens projectdataset [20]. These data include ratings of movies in a 0-5rating scale by a big population of users and have been usedwidely in studies of recommender systems. Each of thesemovies is described by M = 19 thematic tags (e.g., drama,comedy, sports). In our experiments, we analyze differentsamples of 700 users and 10000 items of the catalogue, asretrieved in October 2016.

11

102 103

Cache Capacity

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Cac

he H

it R

atio

R=3

R=5

R=10

102 103

Cache Capacity

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Ca

che

Hit

Ra

tio

R=3

R=5

R=10

(a) rd(u)=0.01, ∀u ∈ U (b) rd(u)=0.1, ∀u ∈ UFig. 4. Experiments with MovieLens traces. Cache hit ratio, H, vs. capacity for different number of recommended items, R. UD (dotted line) andLFU (dash-dot line) are not affected by R, solid lines correspond to CawR and dashed ones to ZD.

In populating our model, we draw on the fact that a userdid rate a specific item, rather than the actual rating (s)heassigned to it. More specifically, the item tags are directlyused to generate the item feature vectors. If an item isdescribed by m different tags, the respective positions ofthe item feature vector are set to 1/m and the remainingones to zero. For instance, if item i is described by “action”and “comedy”, we set f i(j) = 0.5, for those j valuescorresponding to “action” and “comedy”. Then, if Ir(u)is the set of items that user u has rated, we estimate theelement fu(j), j ∈ [1,M ], of user’s u feature vector as

fu(j) =

∑i∈Ir(u)

f i(j)

M∑j=1

∑i∈Ir(u)

f i(j)

. (34)

6.1.2 Synthetic datasets

In this set of experiments, the elements of the two vectorsare populated with values drawn from random probabil-ity distributions (the default one is the standard uniformdistribution). The default parameter values for simulationswith synthetic datasets are |U|=150 users, |I|=1000 itemsand M = 8 thematic areas.

For simulations with both types of datasets, the normal-ized item sizeLi is sampled from a discrete uniform variableU(1, Lmax), with default Lmax = 4.

By Assumption 2.1, we could capture the sensitivity ofrecommendations’ impact to the ranking of items in differ-ent ways. One possibility is to model precu after a geometricdistribution Geom(p) and tune its success probability pa-rameter p to control its skewness. If an even more moderatevariation of this impact with the item rank is needed, wecan log-transform the probabilities of the geometric rankingmodel and normalize them to get a probability distribution.The experiments could be adapted further to experimentalinputs, for instance those in [14], where it is reported thatabout 50% of the YouTube viewers select an entry from thetop five ”related videos” and more than 70% of them do sofrom the top 10 video items. We could tune the geometricparameter p to approximately match these requirements.

Despite the many possibilities that exist, our baselineassumption in our experiments is that recommendations

provide all R items in the list with an equal boost

precu (i) = 1/R, (35)

which fades out with R. The intuition is that the fewer therecommendations are, the less cognitive load they demandfrom users to process them, and the more significant theirimpact is on the eventual user content requests. This as-sumption is more realistic for users accessing content fromlarge-display devices, where it is more comfortable to scrolldown the recommendations’ list.

The choices of user recommendation weights, wru, are

aligned with experimental evidence in [14], according towhich YouTube users request one of the top 10 recom-mended items with a probability that varies in [0.5, 0.7].Thus, in our experiments the user recommendation weightsare sampled from U(0.5, 0.7).

6.2 Trace-Driven simulations

Figs. 4 and 5 validate the performance bounds we foundanalytically for the cache hit ratio under CawR in section5. The extent to which these bounds are tight depends onthe number of issued recommendations per user, R, and thepreference distortion tolerance parameter, rd.

6.2.1 The impact of the number of recommended items oncache hit ratioOn the one hand, R does not affect the performance of UDand LFU schemes. On the other hand, the achievable cachehit ratio under CawR and ZD deteriorates with higher Rvalues. Intuitively, as the recommendation effect is spreadacross more items, some of it is wasted because it gets harderto find R cached items within the users’ recommendationwindow (in the case of CawR) and among the top-R itemsin their preferences (in the case of ZD). Hence, the upperbound becomes looser as the number of recommendationsgrows. Interestingly, so does the lower bound when therelative gain of CawR over the zero-distortion scheme growswith R. This is the case as far as the size of the recommen-dation window size Ku is higher than R so that CawR hashigher chances to find a cached item to recommend. ForR = 10 and rd=0.01, ZD performs up to 16.6% worse thanCawR in terms of cache hit ratio, especially for really smallinstances of cache capacity (Fig. 4a). For rd=0.1, this gapgrows to 121% (Fig. 4b). At the same time, CawR reaches

12

102

Cache Capacity

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

Cac

he H

it R

atio

rd=0.01

rd=0.02

rd=0.05

rd=0.1

102 103

Cache Capacity

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Cac

he H

it R

atio

rd=0.01

rd=0.02

rd=0.05

rd=0.1

(a) R = 3 (b) R = 10Fig. 5. Experiments with MovieLens traces. Cache hit ratio, H, vs. capacity as a function of the preference distortion tolerance, rd (identical for allusers). Dotted and dashed lines correspond to the UD and ZD scheme, respectively. The four intermediate curves correspond to CawR.

100 200 300 400 500 600 700 800 900 1000

Cache Capacity

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Ca

che

Hit

Ra

tio

I=1.000

I=10.000

100 200 300 400 500 600 700 800 900 1000

Cache Capacity

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Ca

che

Hit

Ra

tio

U=700

U=100

(a) R = 10, rd =0.01, U=700 (b) R = 10, rd =0.01. I = 10000Fig. 6. Experiments with MovieLens traces. Cache hit ratio, H, vs. capacity as a function of catalogue size (left) and number of users (right). Dottedlines correspond to the UD scheme, dashed to the ZD scheme and solid lines to CawR.

the 96% and 97% of the performance of the UD scheme,for rd=0.01 and rd=0.1 respectively, and realistic cache ca-pacities (Fig. 4a-4b). An alternative way to quantify thebenefits of our algorithm is by looking into cache capacityrequirements. For rd=0.01, ZD needs up to 35% more cachecapacity than CawR to reach the maximum achievable cachehit ratio when R=10 (Fig. 4a). For rd=0.1, this value climbsto 147% (Fig. 4b).

In all cases, the LFU scheme is significantly outper-formed by schemes that use recommendations.

6.2.2 The impact of the preference distortion tolerance, rd,on cache hit ratioThis enhanced flexibility of CawR is also the reason why itapproaches the upper bound faster (i.e., for smaller cache)when rd=0.1 (Fig. 4b), increasing its advantage over the ZDscheme that is insensitive to rd.

The only scheme that is affected by the preference dis-tortion tolerance parameter is CawR. Higher values of rdprovide the scheme with more flexibility in recommendingitems that are simultaneously parts of the cache placementand the user recommendation windows. Hence, as can beseen in Figs. 5(a-b), but also in Figs. 4(a-b), the CawRperformance increases monotonically with rd moving awayfrom its lower bound (ZD scheme) towards its upper bound(UD scheme). Indicatively, for R = 3 and rd = 0.1, weevidence with CawR cache hit ratios up to 71% higherthan those under the ZD scheme at very small caches (Fig.5a). The respective performance gain increases to 121% forR = 10 (Fig. 5b).

Regarding cache capacity requirements, even for distor-tion tolerance values smaller than rd = 0.01 and R = 3,CawR needs up to 35% less storage capacity to converge tothe upper bound confronted to the ZD scheme. This gainescalates up to 65% when rd = 0.1 (Fig. 5a).

6.2.3 The impact of cache capacity, catalogue size, andnumber of users on cache hit ratioA final set of experiments with the MovieLens traces ad-dresses basic scaling properties of the algorithm, i.e., howthe cache hit ratio varies as a function of the content cata-logue size, cache size, and population of users.

Figs. 6(a-b) report the positive impact of ratio

α =cache capacity

catalog size=

C

|I|(36)

on the cache hit ratio. We further notice that the CawR andthe ZD schemes approach the hit ratio of the UD schemeslower when compared to a system with fewer items.

6.3 Simulations with synthetic datasetsIn this subsection, we explore how the performance ofour algorithm is affected by the sensitivity of users torecommendations and the heterogeneity in their contentpreferences.

6.3.1 User recommendation weightsIn the experiments of this subsection we consider two sce-narios for the range of the user recommendation weights wr

u

13

20 30 40 50 60 70 80 90 100

Cache Capacity

0

0.1

0.2

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Fig. 7. Experiments with Synthetic datasets. Cache hit ratio vs. ca-pacity as a function of user recommendation weights, R=10, rd=0.01,|I|=1.000 items. Dotted lines correspond to the UD scheme, dashedlines to ZD, dash-dot lines to LFU, and solid lines to the CawR.

in (3), namely wru ∈ [0, 0.2] and wr

u ∈ [0.5, 1]. The achievedcache hit ratio for each scenario is shown in Fig. 7.

As is expected, for small recommendation weights,the cache hit ratio under all recommendation schemesis small and comparable to that achieved under therecommendation-agnostic LFU scheme. However, CawR re-mains attractive when cache space is a concern. With storagespaces smaller than the 5% of the total catalogue size, CawRscores similarly to the ZD scheme, needing up to 35% lesscache capacity. Compared to the UD scheme, CawR reachesthe 89% of the performance of the UD scheme, performingalways more than 14% better than ZD.

On the contrary, for larger recommendation weight val-ues, UD, ZD and CawR schemes differ more clearly fromeach other. The cache hit ratio under CawR is 33% higherthan under ZD, for modest cache capacities in the order of2% of the catalogue size. In terms of cache capacity, CawRequals ZD needing up to 32% less cache capacity even forcapacities lower than the 2% of the total catalogue size.Compared to the UD scheme, for high recommendationweights, CawR reaches the 97% of the performance of theUD scheme, performing always more than 6% better thanthe ZD scheme. Overall, Fig. 7 indicates that the more usersassign importance to recommendations made to them, thehigher the advantage of our algorithm over the “honest”recommendation scheme.

6.3.2 Heterogeneity in user content preferences

The heterogeneity in user content preferences can manifestitself in multiple ways. To control this heterogeneity, wegenerate the user content preference distribution as a convexcombination of two distributions: a user-specific componentpegou , which is modeled as described earlier in section 2.2;and a second user-agnostic probability distribution, pext,which is modeled after a Zipf distribution, in line withexperimental evidence in [21] and [22]. The preference ofuser u for item i is then given by:

pprefu (i) = weu · pegou (i) + (1− we

u) · pext(i). (37)

The rationale for introducing pextu is that user preferencesemerge as the combined result of individual preferences andexternal promotional and marketing actions that set globaltrends in content popularity. The weight we

u captures how

these two influences mix for user u. Smaller weu values em-

phasize the component distribution that is common acrossusers, smoothing out the intrinsic user heterogeneity.

We have experimented with different values for wue . In

Fig. 8a we depict results from experiments where wue = 0

(’o’) and wue = 1 (’*’), ∀u ∈ U . For we

u = 0 the three schemesthat issue recommendations collapse to one. Moreover, thetotal achieved cache hit ratio is higher when the contentpreference distributions are homogeneous (we

u = 0 ∀u ∈ U ).Both remarks can be explained intuitively since, in the ratherextreme case where we

u = 0 ∀u ∈ U , the recommendationsissued by the three schemes to the users are identical andfor the R most popular items in the cache.

A second experiment with user heterogeneity concernsthe impact of the content preference distribution. Namely,we let the three functions shown in Fig. 8b serve as theuser content preference distributions, permuting the orderof items for each one of them. The functions include a Zipfdistribution with skewness parameter α=1 (’o’), a uniformdistribution over all items (’+’), and the distribution thatemerges when the elements of the user feature vector fu aredrawn from the standard uniform distribution (’*’).

Although the skewness of the last two distributions issimilar, the achieved cache hit ratio, when the demanddistributions follow them, is very different. When the de-mand is equally split over all items, the cache hit ratio ishigher than when users’ preferences are equally split overfeatures. In the first case, the recommendation window ofevery user will contain the entire catalogue. Hence, CawRexhibits the highest possible flexibility when choosing itemsto recommend and cache. On the contrary, since the items inthe catalogue can be very different, when user preferencesare randomly spread among features, dissimilarities doemerge in the demand. Finally, the lowest cache hit ratioemerges when demand distributions follow a Zipf law withskewness parameter equal to unity. Such a result is expectedfrom Proposition 5.6. These results essentially confirm thatthe performance of CawR, much as that of other cachingschemes, is quite sensitive to the shape of the original usercontent preferences, which set hard bounds on what isachievable.

In Fig. 8c we only plot the cache hit ratio achieved byCawR, but its comparative advantage over ZD still holds.It is more pronounced for Zipf distributions with higherskewness paramater a and fades out as a tends to zero,inline with the prescriptions of Proposition 5.6.

7 MODEL EXTENSIONS AND FUTURE WORK

7.1 Quantifying the distortion of user preferencesIn our analysis, the distortion of user preferences is definedin (4) as the normalized difference between the sums of pref-erence probabilities for the actually recommended items andthose recommended by the “honest” recommender system.This is clearly only one of many possible alternatives forquantifying the distance between the two sets of items.

In the current formulation of the JCRP, the distortionconstraint is conservative. Any choice of items within therecommendation window will satisfy it; but so do combi-nations of items, some of which lie outside this window.In other words, the recommendation window, as defined in

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20 30 40 50 60 70 80 90 100

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100 101 102 103

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unif features

unif items

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Zipf (α = 1)

unif features

unif items

(a) R = 3, rd = 0.01 (b) Content preference distributions (c) R = 5, rd = 0.01

Fig. 8. Experiments with Synthetic datasets. Cache hit ratio vs. capacity as a function of content preference heterogeneity (a,c) and contentpreference distributions (b). On the left plot, dotted lines correspond to the UD scheme, dashed lines to ZD, dash-dot lines to LFU, and solid linesto the CawR. All schemes are depicted for homogeneous (’o’) and heterogeneous (’*’) user demand distributions. On the central, we depict threedifferent pprefu distributions (log-log-scale). On the right, the cache hit ratio under CawR is plotted for the three distributions in (b)

(4) and (10), marks a sufficient but not necessary conditionfor bounding the distortion of the original user contentpreferences by rd.

One apparent alternative would be to get rid of the hardnotion of recommendation window and allow arbitraryselections of recommended items as far as the distortionmeasure does not exceed a certain threshold. Then in theformulation of the optimization problem in section 3, wewould replace the requirement i ∈ Wu in (9) with anadditional constraint

1−

∑i∈I

xuipprefu (i)

R∑i=1

pprefu (i)

≤ rd(u). (38)

Although this may sound more intuitive, in practice it in-troduces considerable amount of computational complexityto the solution of (9). Specifically, the choice of items wouldbecome a demanding combinatorial problem for non trivialinstances.

7.2 Future work

Understanding the precise way recommendations shapeindividual content preferences is a research thread per se,mainly pursued in the context of marketing and recom-mender systems (e.g., [23]). A plausible direction for futurework consists in translating these largely experimental find-ings into solid models and validating our findings in thispaper with them as starting points. This should address thehuman behavior heterogeneity, possibly leveraging data-driven machine learning techniques and principles frombehavioral science.

In this work we consider one round of interaction be-tween the users and the system. An interesting extensionwould be to consider how the dynamics of this interactionevolve in the long-term under such recommendations (e.g.,in [24] phenomena such as attraction or aversion to rec-ommendations, as well as social influence from the user’senvironment are studied) , addressing aspects like the trustusers build in the system and including possible systempenalization (e.g., churn effects). In a fully transparent sys-tem, where users are aware of the nudging recommendation

practices, users might even choose themselves and trade thedistortion their recommendations will undergo.

From the network/system point of view, a basic as-sumption for our analysis has been that the caching andrecommendation decisions are made independently in eachcache-enabled base station. Users are associated with asingle cell according to a content-unaware criterion such asthe received signal strength. An obvious problem extensionwould be to let users associate with multiple cells simultane-ously, and access content dynamically from different caches.This setting would call for jointly optimizing the contentcaching, routing and recommendation decisions.

8 RELATED WORK

Caching is a classic theme in data networking that hasrecently been experiencing a new research thread in the con-text of 4G and 5G mobile cellular networks and their smallcell architectures [18]. One of the major concerns in thesesettings is how the user demand and content popularitycan be accurately predicted. Besides the temporal localityof content demand [8], such predictions should account foruser mobility and the small user populations that small cellcaches present. To this end, proactive (e.g., [9], [10], [25]) andreactive (e.g., [26], [27]) caching approaches are proposed.

In [25], the authors use data from a network operator andmachine learning tools to predict content popularity andproactively fetch content to cell caches. In [10] authors studythe problem of the optimal proactive caching, where futuredelay-intolerant data demands can be served within a givenprediction window ahead of their actual time-of-arrival tominimize service costs. In [9] a hierarchical network con-sisting of a server connected to a number of cache-enablednodes is considered. Authors study the problem of proactiveretention aware data caching, which minimizes the storageand download cost subject to node capacity constraints.In [26] caching decisions are driven by a threshold-basedpolicy: an item is cached after it is requested more timesthan a threshold. The authors experimentally show thatproperly tuning this threshold can reduce the fraction ofthe requested items that are inserted into the cache andonly modestly increase the cache miss ratio. In [27] thispolicy is analyzed in the context of small user populations

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and is shown to be asymptotically optimal regarding thecache hit rate. Their results further show that while a globalcache learns faster, the local caches can be more accurate.At the same time, the combination of small with macrocells yields further possibilities to coordinate caching withcontent routing through different cells, as shown in [6].

Much sparser is the literature on the interplay betweencaching and recommender systems, which is the core themeof our paper. To the best of our knowledge, they are jointlyconsidered in [13], [14], [28], [29], [30], [31], [32]. The firstfour are concerned with video traffic, whereas the restaddress generic content.

The authors in [13] appear to be the first who basecaching decisions on personalized recommendations issuedby recommender systems. They use synthetic datasets tocompare their recommendation-driven caching scheme witha conventional popularity prediction one. They report smallgains for their scheme that disappear in practical scenarioswith ten or more users served by the cache. In [28], theauthors derive conditions under which it pays off to lookinto the spatial variation of content demand and fill thecache with content that is locally, rather than globally, mostpopular. Recommendation-based techniques are proposed,albeit not quantitatively evaluated, also in [30]. The aim is todetermine how to replicate content within a CDN. Commonto [13], [28], [30] is the fact that recommender systems areused as proxies for inferring the content popularity. Weare distinctly different from them, regarding the way weapproach recommender systems: not just as alternative pre-dictors of content demand but also as demand-shaping toolsthat can actively be used to trade-off user- and network-centric performance objectives. In fact, our approach toincreasing the utility of cache content could be seen asdual to the one taken by these three studies. Rather thanstruggling for accurate predictions of the users demand forcontent, our algorithm nudges the users demand towardscontent items that are common in their preferences.

Hence, conceptually most relevant to our work are thestudies in [14], [29], [31], [32], [33]. In the empirical study of[14], the authors achieve an increase of the YouTube cachehit ratio by reordering the videos shown to the users underthe Related Videos list so that already cached ones occupythe first positions. In [31], the authors work with peer-to-peer (P2P) systems and propose heuristic recommendationalgorithms accounting for both the content disseminationcosts and user preferences. In [32] a proactive resource al-location and demand shaping framework is presented. Theauthors analyze theoretically the delivery costs and theirreduction through proactive caching. In their recommendersystem, they modify the ratings shown to users in order toenhance the certainty of user demand. The ”soft cache hits”in [29] are motivated by the entertainment-oriented contentconsumption in current Internet. The idea is to recommendalternative (cached) content to users who request contentnot placed in the cache. The authors present a variety ofoptimization problems regarding soft-hits and cache place-ments in wireless environments and algorithms to solvethe proposed problems. In [33] authors propose modelsand optimization problems that aim at better understandingthe relation between recommendation systems and caching.They consider different caching schemes and present some

preliminary results with the MovieLens dataset, concludingthat recommendation could improve caching performance.

Compared to [14], [31], [33] and [32], we focus on wire-less networks. Authors in [10] also aim at the enhance of thecertainty of the users’ demand. Compared to all previousworks, we formalize the joint caching and recommendationproblem under the assumption of personalized recommen-dations, i.e., different items are recommended to each user.We also introduce the distortion tolerance metric in order toshape content demand in favor of the caching performance.Our results in sections 5 and 6 suggest that the proposedapproach could yield significant gains for the network per-formance and the users satisfaction without disrespectingtheir individual preferences.

9 CONCLUSIONS

Our work in this paper is motivated by the trend thatwants both content providers and network operators alsoassuming roles in content delivery by owning and man-aging content delivery networks. We have looked into thepossible benefits that can arise for the end users and thenetwork when there is some coordination between recom-mender systems and caching decisions. This coordination,at least in this work, implies that recommender systemsactively engineer the recommendations issued to users inways that enhance the caching performance. Practically, thisengineering consists in recommending content that may notnecessarily rank top in the inferred user content preferencesbut still score high in them. By carefully nudging the indi-vidual user demand towards content that attracts preferencefrom many users, the recommender system can result inhigher cache hit ratios and enhanced QoE for end users.

Practitioners in areas like e-commerce are more famil-iar with this demand-shaping (more broadly: behavior-shaping) dimension of recommendations. There is strongevidence that the willingness to consume can be affectedby online recommendations [23]. Their manipulation thereaims at nudging consumers to spend more on productsand services. We rather advocate their “manipulation” for“good” purpose, as an additional network traffic engineer-ing tool that can be used to jointly optimize or balance user-and network-oriented performance objectives.

We have attempted to show this potential in the contextof wireless networks with small cells. At the same time,we tried to explicitly and systematically address ethicalconcerns that are raised by this approach. Simulation re-sults show that the proposed caching-aware recommendersystems bring significant caching performance gains thatpersist over a broad range of parameters for the diversityin users’ preferences, the capacity of caches, the number ofrecommended items and the content catalogue size.

ACKNOWLEDGMENTS

This research has been co-financed by the OperationalProgram ”Human Resources Development, Education andLifelong Learning” and is co-financed by the EuropeanUnion (European Social Fund) and Greek national funds.The authors wish to thank Prof. Stratis Ioannidis for usefuldiscussions.

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Livia Elena Chatzieleftheriou received herDiploma degree in Applied Mathematical andPhysical Sciences from the National TechnicalUniversity of Athens (NTUA), Greece, in 2015.She is currently a Ph.D. candidate at the Depart-ment of Informatics, Athens University of Eco-nomics and Business (AUEB), Athens, Greece.Her research interests are in the area of wirelessnetworks, caching and recommender systems.

Merkouris Karaliopoulos is a Senior Re-searcher with the Department of Informatics, inthe Athens University of Economics and Busi-ness, Greece. He was awarded his Diploma inElectrical and Computer Engineering from Aris-totelian University of Thessaloniki, Greece, in1998, and his PhD in the same field from theUniversity of Surrey, UK, in 2004. He spent oneyear (2006) as postdoctoral researcher in theComputer Science Dept. of University of NorthCarolina at Chapel Hill, NC, USA; three years

(2007-2010) as Senior Researcher and Lecturer in the Swiss FederalInstitute of Technology (ETH Zurich), Zurich, Switzerland; three yearswith the Department of Informatics and Telecommunications, in theUniversity of Athens, Greece, two of which (2010-2012) under an Intra-European Marie Curie Fellowship; and two years (2013-2015) as aResearch Fellow with the Information Technology Institute of the Centerof Research and Technology Hellas (CERTH-ITI), Thessaloniki, Greece.His research interests lie in the broader area of wireless networking andperformance analysis.

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Iordanis Koutsopoulos received the Diplomadegree in Electrical and Computer Engineeringfrom the National Technical University of Athens(NTUA), Greece, in 1997 and the M.S and Ph.D.degrees in Electrical and Computer Engineeringfrom the University of Maryland, College Park(UMCP), MD, USA, in 1999 and 2002, respec-tively. He is now Associate Professor at theDepartment of Informatics, Athens University ofEconomics and Business (AUEB). He was As-sistant Professor (2013-2015) with AUEB. Be-

fore that, he was Assistant Professor (2010-2013) and Lecturer (2005-2010) with the Department of Computer Engineering and Communica-tions, University of Thessaly.

He received the single-investigator European Research Council(ERC) competition runner- up award for the project RECITAL: ResourceManagement for Self-coordinated Autonomic Wireless Networks (2012-2015). His research interests are in the general area of network con-trol and optimization, with applications on wireless networks, socialand community networks, crowd-sensing systems, smart-grid and cloudcomputing.