A General Framework for Fairness in Multistakeholder Recommendations
AA General Framework for Fairness in MultistakeholderRecommendations
Harshal A. Chaudhari ∗ Boston UniversityBoston, [email protected]
Sangdi Lin
Zillow GroupSeattle, [email protected]
Ondrej Linda
Zillow GroupSeattle, [email protected]
ABSTRACT
Contemporary recommender systems act as intermediaries onmulti-sided platforms serving high utility recommendations fromsellers to buyers. Such systems attempt to balance the objectives ofmultiple stakeholders including sellers, buyers, and the platformitself. The difficulty in providing recommendations that maximizethe utility for a buyer, while simultaneously representing all thesellers on the platform has lead to many interesting research prob-lems. Traditionally, they have been formulated as integer linearprograms which compute recommendations for all the buyers to-gether in an offline fashion, by incorporating coverage constraintsso that the individual sellers are proportionally represented acrossall the recommended items. Such approaches can lead to unfore-seen biases wherein certain buyers consistently receive low utilityrecommendations in order to meet the global seller coverage con-straints. To remedy this situation, we propose a general formulationthat incorporates seller coverage objectives alongside individualbuyer objectives in a real-time personalized recommender system.In addition, we leverage highly scalable submodular optimization al-gorithms to provide recommendations to each buyer with provabletheoretical quality bounds. Furthermore, we empirically evaluatethe efficacy of our approach using data from an online real-estatemarketplace.
ACM Reference Format:
Harshal A. Chaudhari, Sangdi Lin, and Ondrej Linda. 2020. A General Frame-work for Fairness in Multistakeholder Recommendations. In
Proceedings ofFAccTRec Workshop: Responsible Recommendation (RecSys ’20).
ACM, NewYork, NY, USA, 7 pages. https://doi.org/10.1145/nnnnnnn.nnnnnnn
The rise of e-commerce platforms in the past decade have maderecommender systems ubiquitous over the world wide web. Recom-mender systems typically assist the buyers on a web marketplaceby recommending them items that are closely aligned to their pref-erences, thereby significantly reducing the time required for search.They have been successfully used in several different domains viz.,e-commerce platforms such as Amazon, eBay, etc., media streamingplatforms like Netflix, Spotify, etc., social networks like Facebook,Twitter, etc., as well as the hospitality services like Yelp, Airbnb,etc.Traditionally, such systems have always aimed at maximizingthe utility of recommendations by tailoring them towards the pref-erences of an individual target buyer. Such recommendations are ∗ Work performed during an internship at Zillow Group.
RecSys ’20, September 26, 2020, Worldwide referred to as personalized recommendations . Increasingly, the ad-vent of multi-sided marketplaces such as Airbnb, UberEats, etc. haveshone spotlight on the issue of welfare of other stakeholders, whoare also affected by these buyer-oriented recommender systems.Multi-sided marketplaces, which primarily rely on network effects for growth are therefore increasingly motivated to include theirobjectives in addition to buyers. Providing meaningful exposureto new sellers or niche brands that are attractive to small marketsegments, supporting small businesses as they compete with theconglomerates for buyer attention, etc. are a few objectives impor-tant to the other stakeholders of the platforms. Without explicitlyaccounting for such goals, the recommender systems can cause un-desirable biases, filter bubbles, and contribute to the ‘rich becomericher’ phenomenon on their platforms.In this work, we propose a scalable multi-stakeholder recom-mender system capable of optimizing for multiple criteria acrossdifferent stakeholders. Specifically, we consider individual sellerson the platform as different stakeholders, who would like theiritems to be proportionally represented in the recommendations.This problem has traditionally been formulated as an integer linearprogram [12, 17]. However, the heuristic algorithms used to solvesuch integer programs cannot provide guarantees on the quality ofsolution when compared to the optimal solution. In contrast, weformulate the task as a multi-objective optimization problem con-sisting of submodular stakeholder coverage objective augmentedwith linear (modular) auxiliary objective. This task is solvable ina computationally efficient manner while also providing provableguarantees on the quality of the solution. The main contributionsof our work are: • Formulation of fair multi-stakeholder recommendations as asubmodular maximization problem, capable of incorporatingmultiple auxiliary objectives simultaneously, while providingstrong approximation guarantees on the quality of solution. • Empirical evaluation using data from Zillow, a real estate mar-ketplace.
In addition to extensive literature on personalized recommenda-tions, multi-receiver/multi-provider recommendations, etc., in re-cent years, there is a growing interest in analyzing recommendationsystems under the lens of fairness . In this section, we position ourwork in the context of broad recommender systems and relatedoptimization techniques.
Multistakeholder recommender systems are a broad category ofrecommender systems that involve more than one stakeholders. a r X i v : . [ c s . A I] S e p ecSys ’20, September 26, 2020, Worldwide Chaudhari, Lin and Linda. In their simplest form, the reciprocal recommendation systemsincluding ‘person-to-person’ links on social networks [7], onlinedating [18] and job search platforms [13] are all examples of sys-tems with two stakeholders. We focus on large scale multi-sidedplatforms such as Amazon, Alibaba, Airbnb, etc., connecting sellersto buyers. Ideally, the percentage of items belonging to each sellerin the items recommended to a buyer should be proportional to thenumber of items belonging to the particular stakeholder that arerelevant to the buyer.Solutions to the above challenges using multi-objective optimiza-tion are explored in the works such as [1, 3]. The importance ofprice and profit awareness in the recommender systems is studiedby [9] and [15]. Works like [11, 14, 19] contribute to the very im-portant domain of analyzing the fairness of recommender systems.Ekstrand and Kluver [4] explore the gender-discriminatory effectsof collaborative filtering in book ratings and recommendations.Works like [16] and [10] explore the impact of sensitive variableson the fairness of recommendations systems. Perhaps closest toour objective, the recent work of Sürer et al. [17] imposes fair-ness constraints in terms of minimum coverage of different sellersacross recommendations to all the buyers using sub-gradient basedmethods to reformulate the coverage optimizing integer program.In contrast, our formulation does not impose strict coverage con-straints. Intuitively, in situations where adhering to strict coverageconstraints results in dramatic sacrifice of utility of recommenda-tions, our formulation automatically relaxes such constraints whilestill satisfying strong approximation bounds in regards to qualityof solution. Moreover, our formulation determines recommenda-tions per buyer and can be incorporated into any personalizedrecommendation system in form a post-processing step.
This section reviews some of the recent advances in the field ofsubmodulaar optimization that our method heavily relies on. Filmusand Ward [6] provided one of the earliest methods to maximize amonotone submodular function under matroid constraints. Leverag-ing multi-linear relaxations of submodular functions, Feldman [5]proposed a continuous greedy algorithm that approximately max-imizes an objective comprised of a submodular function and anarbitrary linear function. Recently, scalable greedy algorithms withsimilar approximation bounds, to maximize difference between asubmodular function and a non-negative modular function are de-scribed in [8]. There have been further advances in the field thatprovide computationally faster algorithms with slightly worse ap-proximation bounds [2]. While not an exhaustive list of literaturein the domain of submodular maximization, the scalability andgeneralizability of our proposed formulation is made possible bythe exemplary contributions of the works mentioned above.
We focus on a multi-stakeholder system where an e-commerce plat-form provides recommendations of items from sellers to the buyersbrowsing on the platform. When a buyer submits a search query onsuch a platform, the recommender system suggests relevant items.Without loss of generalizability, we consider each seller on the platform as a stakeholder , and use the two terms interchangeablyhenceforth. In the application discussed in Section 5, we extend thedefinition of stakeholders to include different sources of propertylistings on Zillow, an online real-estate marketplace. As describedin the previous section, the primary objective of our recommendersystem is to ensure that the percentage of items belonging to eachstakeholder in the items recommended to a buyer is proportionalto the number of items belonging to the particular stakeholder thatare relevant to the buyer. Henceforth, we refer to this objective asthe coverage objective . In addition to the coverage objective, a plat-form can have secondary objectives such as minimizing logisticalcosts, maximizing utility of recommendations, etc., referred to as auxiliary objectives . We aim to optimize the recommender systemsuch that it achieves an optimal trade-off between both of theseobjectives.Next, we formally define our problem setup. Let B = { , · · · , m } be the set of buyers and U = { , · · · , n } be the set of items. It shouldbe noted that only a subset of items U b ∈ U from the universe ofcandidate items are relevant to each buyer b . We represent stake-holders as a set of sellers S = { , · · · , t } . For each item u ∈ U , let S ( u ) ⊆ S denote the sellers who store item u in their inventory.Similarly, let U ( s ) ⊆ U be the set of items in the inventory of aseller s ∈ S . The goal of our recommendation system is to suggest k items to the buyer that fairly cover all the sellers, assuming that k ≤ n . When serving recommendations, we use a binary variable x u , s to denote whether an item u is recommended to a buyer coversa seller s i.e., x u , s = u ∈ U ( s ) . To define the stakeholder coverage objective, we first formalize thenotion of fair coverage.
A set of k recommendations denoted by R b given to a buyer b is considered fair to all stakeholders if and onlyif ∀ s ∈ S : (cid:205) u ∈R b x u , s k ≥ | U b ( s )|| U b | . (1)Equation 1 ensures that the percentage of each seller’s inventoryincluded in the recommended items R b is at least as high as thepercentage of the seller’s inventory relevant to the buyer b . Hence-forth, we refer to the ratio | U b ( s )|| U b | as the fair coverage threshold ofseller s for buyer b and denote it by δ s , b . It should be noted thatSürer et al. [17] imposes similar provider constraint across all thebuyers and sellers together: ∀ s ∈ S : (cid:213) b ∈ B (cid:18) (cid:205) u ∈R b x u , s m × k (cid:19) ≥ | U ( s )| n (2)Our definition of fair coverage supersedes such a constraint be-cause ensuring fair coverage for each seller in recommendationsfor every buyer query obviously leads to satisfying the providerconstraint in Equation 2 across all buyers and sellers, but not viceversa. Furthermore, just satisfying provider constraints can lead tobiased situations where individual buyers are consistently providedlow utility recommendations in order to satisfy a global coverageconstraint for a seller. Defining fair coverage on individual buyermakes it possible to augment output of any modern personalizedrecommendation system with our objective in real-time. General Framework for Fairness in Multistakeholder Recommendations RecSys ’20, September 26, 2020, Worldwide
Having defined fair coverage , we are nowin a position to formalize the coverage objective denoted by F ( . ) .For a set of recommendations R b , the value of coverage objectiveis: F (R b ) : = (cid:213) s ∈ S min (cid:18) (cid:205) u ∈R b x u , s k , δ s , b (cid:19) (3)Let us remind ourselves about the submodular functions. A setfunction f : 2 V → R is submodular if for every A ⊆ B ⊆ V and e ∈ V \ B it holds that f ( A ∪ { e }) − f ( A ) ≥ f ( B ∪ { e } − f ( B ) .Lemma 3.1. The coverage objective F ( . ) is a submodular set func-tion. Proof. For a buyer b , consider two sets of items R , R ⊆ U b such that R ⊂ R . Consider an item u ∈ U b \ R . Without lossof generality, we assume that S = { s } i.e., there is a single stake-holder to be covered and u ∈ U ( s ) . This gives rise to two casesenumerated below. Case 1:
The set R provides fair coverage to stakeholder s . Hence, (cid:205) u ∈R x u , s k ≥ δ s , b . Hence, F (R ) = δ s , b . Given that R ⊂ R ,we also know that F (R ) = δ s , b . Moreover, F (R ∪ { u }) = δ s , b and F (R ∪ { u }) = δ s , b . Hence, F (R ∪ { u }) − F (R ) = F (R ∪{ u }) − F (R ) = Case 2:
The set R does not cover the stakeholder s fairly. Hence, (cid:205) u ∈R x u , s k < δ s , b . Hence, F (R ∪ { u }) − F (R ) = / k . If the rec-ommendations R fairly covers the stakeholder s , F (R ∪ { u }) − F (R ) =
0, else, F (R ∪ { u }) − F (R ) = / k .Thus, in both cases, F (R ∪ { u }) − F (R ) ≥ F (R ∪ { u }) − F (R ) .Hence, proved. Let us denote an auxiliary objective by G ( . ) . We differentiate thepotential auxiliary objectives into two broad categories viz., maxi-mization objectives and the minimization objectives. Such an auxiliary objective typi-cally involves maximizing an attribute related to the recommendeditem alongside the primary objective of fair multi-stakeholder cov-erage. For example, maximization of the utility of recommendations.All modern personalized recommender systems typically compute autility score r u , b denoting the relevance of item u to a buyer b usingvarious models such as collaborative filtering or a content-basedrecommendation system. Thus, total utility of recommended itemsis: G (R b ) : = (cid:213) u ∈R b r u , b (4)As the utility scores are non-negative and computed beforehandand generally fixed for each item, we can assume that G ( . ) is a mod-ular set function (equality in the submodular function definition).Note that the objectives like maximization of non-negative fixedattributes such as profit margins, etc. can be incorporated similarly. Next, we consider the scenario re-quiring minimizing an attribute related to the recommended itemswhile simultaneously attempting to maximize the fair coverageobjective. For example, one can envision a user-oriented goal that recommends items to a buyer that have minimum cost per unitutility. In contrast to the utility maximization objective above, wewould like to minimize the cost per unit utility of recommendations.Hence, G (R b ) : = (cid:213) u ∈R b c u / r u , b (5)where c u is the cost of an item. Combining the stakeholder fair coverage objective with the auxil-iary objectives above, we obtain the overall objective in the form F α (R b ) : = αF (R b ) ± ( − α ) G (R b ) (6)where α ∈ [ , ] allows us to control the trade-off between thetwo objectives. Note that we add the two objectives when dealingwith a maximization auxiliary objective, and take the difference incase of a minimization auxiliary objective. A reader may correctlywonder the need for differentiation between the maximization andminimization auxiliary objectives, since typically the two are inter-changeable with a change of sign. However, in our case, as describedin the subsequent sections, the nature of auxiliary objectives af-fects the properties of the overall combined objective F α ( . ) , andsubsequently the optimization algorithms. Hence, we differentiatebetween the two.Problem 1. Given a set of buyers B , a set of items U , a set ofstakeholders S and platform parameter α , recommend a set of items R ∗ b to each buyer such that: R ∗ b = arg max R b ⊆ U b F α (R b ) s.t., |R b | = k . (7)In the following section, we show how existing contributions fromthe field of submodular optimization can be used to optimize thecombined objective with strong approximation guarantees. In this section, we describe the two principal algorithms that weuse to optimize the overall objective formulated above.
First, we account for the case where the auxiliary objective is maxi-mization of a non-negative modular set function, described in sec-tion 3.2.1. It can be trivially shown that the corresponding overallobjective function obtained in this situation is a monotone submod-ular function. Such a function can be maximized using a simplegreedy approach in Algorithm 1 that builds the recommended itemsset iteratively. Let us denote the marginal gain of adding a new itemto a set of recommendations by F α ( u |R b ) = F α (R b ∪{ u })−F α (R b ) .In each iteration, the greedy Algorithm 1 simply adds to the setthe item with the largest marginal gain. Moreover, the solutionprovided by the greedy algorithm satisfies strong approximationguarantee. F α (R b ) ≥ ( − e )F α (R ∗ b ) where R ∗ b is the optimal solution for the Problem 1 with a maximiza-tion auxiliary objective. Notably, for each buyer b , the algorithm ecSys ’20, September 26, 2020, Worldwide Chaudhari, Lin and Linda. ALGORITHM 1:
Greedy Input : Set of relevant items for buyer U b , fair coveragethresholds δ s , b for each seller, k , α ; Output : Set of recommended items R b ; R b = ∅ ; while |R b | ≤ k z = arg max u ∈ U b F α ( u |R b ) ; R b ← R b ∪ { z } ; U b ← U b \ { z } ; return R b iterates through all candidate items on line 5 to find the item withthe largest marginal gain, resulting in a time complexity of O ( nk ) per buyer, not accounting for the complexity of evaluating thecoverage objective itself.In online personalized recommender systems with thousands ofpotential items, such an approach can potentially increase responsetimes, when set of recommendations are updated continuouslybased on user activity within a session. For such applications, wemay achieve a significant speed-up without a loss of quality ofthe solution by using a priority heap to avoid re-computation ofmarginal gain of all items, as shown in Algorithm 2.On account of submodularity, the marginal gain of elements canonly decrease in each iteration. Leveraging this observation, weonly need to re-evaluate the marginal gains of a small subset ofitems per iteration, until the item whose marginal gain computedin the previous iteration is less than the updated marginal gain ofthe top-most element in the priority heap as shown on line 8 ofAlgorithm 2. It should be noted that the worst case complexity ofAlgorithm 2 is the same as that of Algorithm 1. But in most practicalapplications, it is significantly faster. Next, we describe the algorithm for the situation where the auxiliaryobjective is a minimization of a non-negative modular set function,described in Section 3.2.2. The main challenge in such cases isthat the function αF (R b ) − ( − α ) G (R b ) can be either positiveor negative, making the overall objective function non-monotone.However, very recent work of Harshaw et al. [8] provides us withtheoretically guaranteed fast algorithms for such an objective. Thereason a standard greedy algorithm fails to optimize such an ob-jective is described below. Suppose there is a ‘bad item’ u whichhas highest overall marginal gain F α ( u | ∅ ) and so is added to therecommended items set; however, once added, the marginal gainof all remaining items drops below their corresponding auxiliaryobjective value, and so the greedy algorithm terminates. This issub-optimal when there are other elements v that, although theiroverall marginal gain F α ( v |R b ) is lower, have much higher ratiobetween the coverage objective and the auxiliary objective.To resolve this issue, Harshaw et al. use a distorted greedy cri-terion as shown in line 5 of Algorithm 3 which gradually placeshigher relative weight on the stakeholder coverage objective whencompared to the auxiliary objective as the algorithm progresses.However, it should be noted that since the overall objective can ALGORITHM 2:
Lazy Greedy Input : Set of relevant items for buyer U b , fair coveragethresholds δ s , b for each seller, k , α ; Output : Set of recommended items R b ; R b = ∅ ; Create maximum priority heap H and push each key u from U b with value v u = F α ( u |∅) ; while |R b | ≤ k Pull top key i from the priority heap H ; Evaluate new marginal gain F α ( i |R b ) , Φ = { i } ; while True Pull top key j from the priority heap with value v j ; if F α ( i |R b ) ≥ v j break; else Φ ← Φ ∪ { j } ; z = arg max i ∈ Φ F α ( i |R b ) ; R b ← R b ∪ { z } ; Φ ← Φ \ { i } ; for each j ∈ Φ Re-insert key j into the heap H with value v j = F α ( j |R b ) ; return R b be negative, we only recommend items with a positive distortedgain as shown in line 6 of the algorithm. Hence, for certain valuesof α , we may encounter a situation where the recommendationsprovided by the algorithm are less than k . Using Theorem 3 ofHarshaw et al. [8], it can be shown that Algorithm 3 provides asolution R b for each buyer such that, F α (R b ) ≥ ( − e ) αF (R ∗ b ) − ( − α ) G (R ∗ b ) . (8)Intuitively, this guarantee states that the value of overall objective isat least as much as would be obtained by recommending items of thesame cost as the optimal solution, while gaining at least a fraction ( − / e ) of its stakeholder coverage. Furthermore, Algorithm 3 timecomplexity can be improved by sampling the items from which thebest item is chosen in each iteration (line 5). Theorem 4 of Harshaw et al. [8] shows that, if we sample uniformly and independently (cid:108) |R b | k log (cid:0) ϵ (cid:1)(cid:109) items from U b in each iteration to maximize over,we can reduce the time complexity to O ( n log ( / ϵ )) where ϵ is anerror parameter, while achieving the same performance guaranteein expectation. E [F α (R b )] ≥ ( − e ) αF (R ∗ b ) − ( − α ) G (R ∗ b ) . (9)The sampling version of Algorithm 3 is referred to as ‘StochasticDistorted Greedy’. One may envisage an application where there are multiple auxil-iary objectives. Algorithm 2 can optimize multiple maximizationobjectives together. On the other hand, Algorithm 3 can optimize
General Framework for Fairness in Multistakeholder Recommendations RecSys ’20, September 26, 2020, Worldwide
ALGORITHM 3:
Distorted Greedy (Harshaw et al. [8]) Input : Set of relevant items for buyer U b , fair coveragethresholds δ s , b for each seller, k , α ; Output : Set of recommended items R b ; R b = ∅ ; for i = to k − z = arg max u ∈ U b (cid:26)(cid:0) − k (cid:1) k −( i + ) αF ( u |R b ) − ( − α ) G ( u ) (cid:27) ; if (cid:26)(cid:0) − k (cid:1) k −( i + ) αF ( u |R b ) − ( − α ) G ( u ) (cid:27) > R b ← R b ∪ { z } ; U b ← U b \ { z } ; return R b multiple minimization objectives simultaneously. Combination ofdifferent maximization and minimization objectives together posesan interesting dilemma. For example, consider an auxiliary objectiveof the form: G (R b ) = β (cid:213) u ∈R b r u , b + β (cid:213) u ∈R b (− c u ) + β · · · where β i ∈ [ , ] controls the relative importance of the auxiliaryobjectives. In applications where the individual auxiliary objectivesare fixed (i.e. known in advance), the operator can verify in aheadof time if G (R b ) is non-negative and use the appropriate algorithm.An interesting situation arises if the auxiliary objective value foreach item is not fixed. For the purpose of brevity, we do not discusssuch a situation in this work. However, an enterprising reader mayrefer to the Continuous Greedy algorithm proposed by Feldman [5].It maximizes the multi-linear extension of the coverage objective alongside an arbitrary linear auxiliary objective, and follows it withPipage rounding procedure to obtain a discrete solution with strongapproximation guarantees, as described in Feldman [5].
In this section, we begin by describing the data obtained fromZillow, an online real estate marketplace, and then we evaluate theperformance of our proposed approach.
Real estate buyers visiting the Zillow website are typically showna paginated list of recommended property listings satisfying thevarious filter criteria within the searched region. Zillow uses itsproprietary algorithms to personalize recommendations to potentialbuyers based on their search criteria. The top listings recommendedto the potential buyers are typically obtained from various sources.Majority of the properties on the platform are listed by independentthird-party realtors, alongside ‘New construction homes’ listed bybuilders, as well as Zillow owned homes. Furthermore, some ofthese listings have various attributes such as availability of 3D orvideo tours available to the potential buyers. It is in this context thatZillow is faced with the multi-stakeholder recommender system.In this application, we consider a random sample of over 13,000search sessions obtained from buyer interactions on the website. After applying the filters set by the buyers during these search ses-sions we end up with a collection of over 36,000 potential candidatelistings. In this setting, we consider 5 different stakeholders viz., independent listings, new constructions, Zillow owned, 3D homes and video tours.
It should be noted that a single listing can potentiallybelong to multiple stakeholders. For example, a new constructionhome listing may sometimes have an accompanying 3D home tour.Each listing has a fixed dollar cost and an associated buyer specificutility score. As a platform operator, our objective is to recommendeach buyer 20 listings that cover the relevant stakeholders fairly asdefined in Section 3.1.1.
For all the experiments, we run a mul-tiprocessing Python implementation of the algorithms where eachprocess independently recommends items for an individual buyer.All the results presented below reflect the evaluation of the objec-tives based on a uniform random sample of 1000 sessions and theirassociated listings. Although our application has a limited numberof stakeholders, as the computation of the coverage objective islinear in the number of stakeholders, our approach does not facescalability issues in situations with a large number of stakeholders.Furthermore, we do not require any extra storage for Algorithm 1and Algorithm 3. In case of Algorithm 2, the extra storage requiredfor the maximum priority heap is O ( n ) . We empirically evaluate the proposed formulation and algorithmsfor fair multi-stakeholder coverage alongside two separate auxiliaryobjectives viz., utility maximization using Algorithm 2 and dollarcost per unit utility minimization using Algorithm 3.
In this experiment, we measure thedifference between the stakeholder coverage achieved by our ap-proach and the desired target coverage required by the fair coverage criterion. Specifically, if we represent the proportion of recom-mended listings belonging to stakeholder s by η s , b and the faircoverage threshold for the same stakeholder by δ s , b as described inSection 3.1.1, then we plot the difference ∆ s , b = ⌈ k ( η s , b − δ s , b )⌉ averaged over all the buyers, for varying values of the parameter α . When ∆ s , b ≥ ∆ s , b < s is under represented in the k recommendations.In Figure 1, we observe that a fair coverage of all stakeholder isachieved for both the auxiliary objectives, as the value of α i.e.,importance of coverage objective increases. Here, we visualize the trade-off be-tween the primary fair coverage objective and the auxiliary objec-tive during utility maximization and cost minimization in Figure 2.For clarity of visualization, we scale the auxiliary objective dur-ing cost per unit utility minimization by multiplying it with 10 − .We clearly see the trade-off between the coverage objective andthe utility of recommendations in Figure 2a. When α =
0, onlythe highest utility listings are recommended. As the value of α increases, the overall utility of recommended listings is slightlysacrificed in order to improve the stakeholder coverage. During thecost per unit utility minimization in Figure 2b, the increase in costof recommendations in order to improve the stakeholder coverage ecSys ’20, September 26, 2020, Worldwide Chaudhari, Lin and Linda. M e a n s , b Zillow offersNew construction3D homes Video toursIndependent (a) Utility Maximization M e a n s , b Zillow offersNew construction3D homes Video toursIndependent (b) Dollar Cost Per Unit Utility Minimization
Figure 1: Fair coverage of stakeholders O b j e c t i v e v a l u e Coverage ObjectiveAuxiliary ObjectiveOverall Objective (a) Utility Maximization O b j e c t i v e v a l u e Coverage ObjectiveAuxiliary ObjectiveOverall Objective (b) Dollar Cost Per Unit Utility Minimization
Figure 2: Trade-offs between coverage and auxiliary objec-tives is not very apparent in this data due to the use of Stochastic Greedyalgorithm with error parameter ϵ = . Lastly, we compare the algorithm run-times per buyer for different objectives in Figure 3. While the worstcase time complexity for Lazy Greedy algorithm is same as thatof Greedy algorithm, we observe that it is significantly faster inpractice. In case of minimization auxiliary objectives, the Stochas-tic Distorted Greedy algorithm with error parameter ϵ = . Maximization Minimization0510152025 R un t i m e ( i n s e c o n d s ) GreedyLazy Greedy Distorted GreedyStochastic Distorted Greedy
Figure 3: Runtime comparison for auxiliary objectives more efficient than the deterministic Distorted Greedy algorithm.Availability of such fast algorithms allows us to use this formula-tion of fair multi-stakeholder coverage in real-time personalizedrecommender systems.
In this work, we study the problem of fair multi-stakeholder rec-ommendations. Our work confirms the idea that formulating multi-stakeholder coverage objective in form of a submodular functionallows us to leverage existing submodular optimization techniquesthat can incorporate commonly used secondary objectives in per-sonalized recommender systems. Using data from an online real-estate marketplace, we empirically evaluated the efficiency andscalability of our proposed approach. Incorporating non-linearsecondary objectives such as learning-to-rank metrics into thisframework remains an open research problem.
REFERENCES [1] Himan Abdollahpouri, Robin Burke, and Bamshad Mobasher. 2017. RecommenderSystems as Multistakeholder Environments. In
Proceedings of the 25th Conferenceon User Modeling, Adaptation and Personalization (UMAP ’17) . ACM, New York,NY, USA, 347–348. https://doi.org/10.1145/3079628.3079657[2] Dmitrii Avdiukhin, Grigory Yaroslavtsev, and Samson Zhou. 2019. "Bring YourOwn Greedy"+Max: Near-Optimal / -Approximations for Submodular Knap-sack. (Oct. 2019). arXiv:1910.05646 [cs.DS][3] R D Burke, H Abdollahpouri, and others. 2016. Towards Multi-Stakeholder UtilityEvaluation of Recommender Systems. UMAP (Extended) (2016).[4] Michael D Ekstrand, Mucun Tian, Mohammed R Imran Kazi, Hoda Mehrpouyan,and Daniel Kluver. 2018. Exploring author gender in book rating and recom-mendation. In
Proceedings of the 12th ACM conference on recommender systems .242–250.[5] Moran Feldman. 2018. Guess Free Maximization of Submodular and Linear Sums.(Oct. 2018). arXiv:1810.03813 [cs.DS][6] Yuval Filmus and Justin Ward. 2012. Monotone Submodular Maximization overa Matroid via Non-Oblivious Local Search. (April 2012). arXiv:1204.4526 [cs.DS][7] Ido Guy. 2015. Social Recommender Systems. In
Recommender Systems Handbook ,Francesco Ricci, Lior Rokach, and Bracha Shapira (Eds.). Springer US, Boston,MA, 511–543. https://doi.org/10.1007/978-1-4899-7637-6_15[8] Christopher Harshaw, Moran Feldman, Justin Ward, and Amin Karbasi. 2019.Submodular Maximization Beyond Non-negativity: Guarantees, Fast Algorithms,and Applications. (April 2019). arXiv:1904.09354 [cs.DS][9] Dietmar Jannach and Gediminas Adomavicius. 2017. Price and Profit Awarenessin Recommender Systems. (July 2017). arXiv:1707.08029 [cs.IR][10] Toshihiro Kamishima, Shotaro Akaho, Hideki Asoh, and Jun Sakuma. 2018. Rec-ommendation independence. In
Conference on Fairness, Accountability and Trans-parency . 187–201.[11] Weiwen Liu and Robin Burke. 2018. Personalizing fairness-aware re-ranking. arXiv preprint arXiv:1809.02921 (2018).[12] Edward C Malthouse, Khadija Ali Vakeel, and Yasaman Kamyab Hessary. 2019.A Multistakeholder Recommender Systems Algorithm for Allocating SponsoredRecommendations. (2019).[13] Tsunenori Mine, Tomoyuki Kakuta, and Akira Ono. 2013. Reciprocal Recommen-dation for Job Matching with Bidirectional Feedback. In
Proceedings of the 2013 Sec-ond IIAI International Conference on Advanced Applied Informatics (IIAI-AAI ’13) .IEEE Computer Society, USA, 39–44. https://doi.org/10.1109/IIAI-AAI.2013.91
General Framework for Fairness in Multistakeholder Recommendations RecSys ’20, September 26, 2020, Worldwide [14] Natwar Modani, Deepali Jain, Ujjawal Soni, Gaurav Kumar Gupta, and PalakAgarwal. 2017. Fairness Aware Recommendations on Behance. In
Advancesin Knowledge Discovery and Data Mining . Springer International Publishing,144–155. https://doi.org/10.1007/978-3-319-57529-2_12[15] Changhua Pei, Xinru Yang, Qing Cui, Xiao Lin, Fei Sun, Peng Jiang, Wenwu Ou,and Yongfeng Zhang. 2019. Value-aware Recommendation based on Reinforce-ment Profit Maximization. https://doi.org/10.1145/3308558.3313404[16] Nasim Sonboli and Robin Burke. 2019. Localized fairness in recommender systems.In
Adjunct Publication of the 27th Conference on User Modeling, Adaptation and Personalization . 295–300.[17] Özge Sürer, Robin Burke, and Edward C Malthouse. 2018. Multistakeholder recom-mendation with provider constraints. In
Proceedings of the 12th ACM Conferenceon Recommender Systems . dl.acm.org, 54–62.[18] P Xia, B Liu, Y Sun, and C Chen. 2015. Reciprocal recommendation system foronline dating. (2015).[19] Sirui Yao and Bert Huang. 2017. Beyond Parity: Fairness Objectives for Collabo-rative Filtering. In