Fairly Recommending with Social Attributes: A Flexible and Controllable Optimization Approach
Authors: Jinqiu Jin
Haoxuan Li
Fuli Feng
Sihao Ding
Peng Wu
Xiangnan He
Venue: NeurIPS 2023 poster (2023)
Keywords: Recommender System
Fairness

Abstract: Item-side group fairness (IGF) requires a recommendation model to treat different item groups similarly, and has a crucial impact on information diffusion, consumption activity, and market equilibrium. Previous IGF notions only focus on the direct utility of the item exposures, i.e., the exposure numbers across different item groups. Nevertheless, the item exposures also facilitate utility gained from the neighboring users via social influence, called social utility, such as information sharing on the social media. To fill this gap, this paper introduces two social attribute-aware IGF metrics, which require similar user social attributes on the exposed items across the different item groups. In light of the trade-off between the direct utility and social utility, we formulate a new multi-objective optimization problem for training recommender models with flexible trade-off while ensuring controllable accuracy. To solve this problem, we develop a gradient-based optimization algorithm and theoretically show that the proposed algorithm can find Pareto optimal solutions with varying trade-off and guaranteed accuracy. Extensive experiments on two real-world datasets validate the effectiveness of our approach.

Fairly Recommending with Social Attributes: A Flexible and Controllable Optimization Approach
Jinqiu Jin
Haoxuan Li Fuli Feng Sihao Ding'
Peng Wu Xiangnan He
University of Science and Technology of China
Peking University Beijing Technology and Business University jjq2002101 50t.00150maaalmmmmmmmm uste. edu. en, hxli@stu. pku. edu. cn, fulifengS3dgmaill com, dsihao@mail, ustc. edu, en, pengwu@btbu, edu. en, xiangnanhe@gmail.com com
Abstract
Item-side group fairness (IGF) requires recommendation model to treat different item groups similarly, and has a crucial impact on information diffusion, consump- tion activity, and market equilibrium. Previous IGF notions only focus the direct utility of the item exposures, Le., the exposure numbers across different item groups. Nevertheless, the item exposures also facilitate utility gained from the neighboring users via social influence, called social utility, such as information sharing on the social media. To fill this gap, this paper introduces two social attribute-awe aware IGF metrics, which require similar user social attributes on the exposed items across the different item groups. In light of the trade-off between the direct utility and social utility, we formulate a new multi-objective optimization problem for training recommender models with flexible trade-off while ensuring controllable accuracy. To solve this problem, we develop a gradient-based optimization algorithm and theoretically show that the proposed algorithm can find Pareto optimal solutions with varying trade-off and guaranteed accuracy. Extensive experiments on two real- world datasets validate the effecttivnness of our approach. Our codes available at httts:///githu: com mwta:mtttmmeeaa com//itaoo-at//ipp2233 attp:aaaoocoaappp...ccsll..aaa
1 Introduction
Developing fair recommendation algorithms is crucial to perform reliable information search and decision making, which prevents users' well as platforms' interests from being sacrificed [ One particular aspect of recommendation fairness is item-side group faimess (IGF), which requires recommendation model to treat different item groups similarly, and the items are grouped based on attributes such as category or brand 2 4 Existing IGF frameworks primarily focus on the direct utility of item exposures, requiring similar number of exposures for different item groups, and can be broadly categorized into two forms: Statistical Parity (SP) 5 o
and Equal Opportunity (EO) (7].
Nevertheless, the existing IGF notions overlook the social utility of item exposures, as users with different social attributes may produce varying utilities due to the social influence among users. For example, user's friends may view recommended micro-video due to sharing activities or public record in the user's ss timeline. This can lead to unfaimeess problem in which some item groups benefit more than others though the existing IGF notions are satisfied. Figure [ illustrates toy example where item group A receives the same number of exposures as group B. thus satisfying the requirement of the previous SP, while items in group A are recommended to users with greater numbers of friends. This motivates us to consider both direct and social utility for IGF notions.
"qqual contribution. CCoresppondig author.
37th Conference on Neural Information Processing Systems (NcurIPS 2023).

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# Exp
# Friends
# Exp
# Friends
Exp
Friends
&&R 8 888
88 8
Item Groups
Item Groups
item Groups
R
R
B
&
B
Direct (2 2)
Social (6+2)
Direct (1++3)
Social (3=3)
Direct (2-2)
Social (4=4)
(a) Previous IGF notions
(b) Social attribule-aware notions
(c)
Multi-objectivv optimization
Figure 1: A toy example with item groups A and B illustrate direct and social utilities of the IGF notions, where "# Exp" is the number of exposed users across the item group, and "# Friends" is the number of friends of the exposed users. The multi-objective optimization considers both utilities.
In this paper, we first introduce two social attribute-aware IGF metrics, namely Neighborhood SP (NSP) and Neighborhood EO (NEO), which require that users exposed to different item groups have similar total social utility. As shown in Figure [b] item groups A and B have the same total social utility, which is measured by the number of friends in this toy example. Compared the previous SP and EO notions, NSP and NEO require similarity in the neighbors of the exposed users, rather than simply requiring the similar number of exposed users across the item groups. However, optimizing only the social attribute-ave aware IGF metrics may result in varying direct utilities across different item groups, e.g., item groups and B in Figure Tb have the different number of exposed users. Therefore, it is reasonable to consider both direct and social utility when developing fair recommender models.
To this end, we next formulate multi-objective optimization problem for training the recommender models with consideration of both direct and social utility, and further require flexibility and control- lability of the trade-offs. Specifically, motivated by the previous study (8). we incorporate pre-defined preference regions with varying trade-offs between the direct and social utility into the multi-objective optimization problem, enabling the flexibility choose the desired trade-off's in practice. Meanwhile, we also incorporate a customizable accuracy constraint for the controllability of the optimization, which leads guaranteed recommendation accuracy while satisfying the IGF notions.
We further propose a Social attribute-aware Flexible fair recommendation training algorithm with controllable Accuracy (SoFA), for solving the above multi-objective optimization problem. Given pre-defined preference region, the proposed gradient- within this region achieve the desired trade-off. On the other hand, when the accuracy loss exceeds a given threshold, the model parameters update direction is changed to achieve the minimum accuracy guarantee. We also theoretically show that SoFA can find Pareto optimal solutions with varying trade-off, meaning the direct and social utility of the trained model is not dominated by any other solutions. Extensive experiments are conducted on real-world datasets with social attributes, and the experimental results validate the effectiveness of the proposed training algorithm.
algorithm updates the model parameters
The main contributions of this paper are summarized as follows:
We propose two social attribute-awarc IGF metrics, named NSP and NEO, to study the item exposure utility gained from the user social network.
We formalize a multi-objective optimization problem to achieve flexible trade-off between the direct utility and social utility with controllable accuracy sacrifice of the recommendation.
We further propose gradient- based optimization algorithm to solve the above problem, called SoFA, and theoretically show that SoFA can find Pareto optimal solutions with varying trade-off
We conduct extensive experiments on two real-world datasets, revealing that methods ignoring social influence would lead to unfair exposure, and validating the effectiveness of our proposal.
2 Preliminaries
In this section, we present the background about personalized recommendation, item-side group fairness including SP and EO notions, and multi-objective optimization.
Personalized Recommendation. Personalized recommendation aims to select a small subset of items to each user based on historical data, with users denoted as Ut {u} and items denoted as

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= In our study, we focus on a common recommendation scenario known as collaborative filtering (CF) with implicit feedback, where the historical data contains the items that each user has
interacted with 2 10 11 12. Bayesian Personalized Ranking (BPR) [9] is one of the representitive CF algorithm modeling the interaction probabilities, by minimizing the pairwise ranking loss
X
min (f)
Σ In (iu.s (u.) + [u.i5]ED
(I)
2
where D denotes the historical data for training, including user u, interacted item i, and no interacted item j. (-) the Sigmoid function, 0 represents the model parameters, and X9 is the regularization hyper-parameter to prevent overfitting. The predicted user preference scores Dv. and Dv.j for positive item and negative item j can computed by using the widely-adopted matrix factorization [3].
Item-Side Group Fairness (IGF). The IGF requires faimess of recommendation holds across a set of item groups 9 = {91. {91.9e.... 92. ................................ J. where each item E I belongs to one or more groups. The group of an item is correspond to attributes such as genre, brand, or other item characteristics, and denote Gg. (i) as the indicator function of whether item belongs to group 9a. i.e, Gg. (i) 1 if i E 9a. otherwise G. (i) O. IGF notions aim to ensure fairness across different groups without over-recommending or redremrncommin any specific group [4] The existing IGF notions mainly focus on the exposure levels across different groups, and can be classified into positive rate-based metrics and confusion matrix- -based metrics [i]. One particular positive rate-based metric is Statistical Parity (SP) 6). which aims to ensure that each group has equal likelihood of being recommended and requires the following quantities to be similar across different item groups
PP (R g - ga) Eneu Eier Gga (i) (u,
for all a a=1,... A,
THEHLiES Go. (1)
where (u, = o (B..:) estimates the interaction probability for user u item i, and EiET Go. (i) is the total number of items belonging to group Ja. Instead, confusion matrix-based metrics further consider the ground truth labels. For instance, Equal Opportunity (EO) 7 aims to ensure the same true positive rate across different item groups
P (R) g = 9a. y = 1) = Eveu EIEr (1) (Q,((,,)) (u, ΣuEu GIEIGGo (u,
for all a a= A, (3)
where Y(u, i) is the ground truth label for user u and item i, and Σier C.. (i)Y (u, i) computes the total number of items that user u has interacted with group Ja. To keep the same value scale for different metrics, we evaluate the IGF of a recommendation model by computing the relative standard deviation of the group probabilities
SP rsd (IP (R g 9 P.. == 9A4).
EO = rsd (IP ( 9 -1.-...-)),--.... , 9A. = 1)).
91.
where rsd(.) = std( / mcan(-) calculates the relative standard deviation. The lower the SP and EO values, the fairer the recommender system satisfies the IGF fairness notions.
Multi-Objective Optimization. In many real-world tasks, there might be multiple optimization objectives rather than single one, while these objectives may collaborate or conflict with each other [ Multi-objective optimization [17] aims to find set of solutions that effectively balance
the trade-off among these objectives, and it has been widely used in areas such as reinforcement learning [18] and E-commerce [9) Typically, a multi-objectivve optimization problem is
min (( (O), C2(0), ... (O))
(5)
where (C,, states the multiple objectives. To solve the multi-objective optimization problem, several population-base based and evolutionary algorithm -baed methods (20 21| 22 have been proposed. Nevertheless, they are not efficient in handling large-scale datasets in recommendation Alternativly,, mulli-objectteo gradient descent approches [23 address this problem by leveraging Karush- Tucker (KKT) conditions 25 to find a gradient direction that reduces all objective values simultaneously. For example, gradient-based steepest descent methods (3 are proposed to seek descent direction d, by solving the following optimization problem
(d,, az) = arg min a d
|dl s.s. V., < a, i. M,
(6)
3

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then updates the model parameters using gradient descent 0:+1 - 0, + nd, with step size Theoretically. the solutions of the descent direction guarantee that all objective values will decrease. thus achieving the Pareto optimality [26). To obtain these descent direction solutions, one can employ the widely-adopted multiple gradient descent algorithm (MGDA) 24
3 Social Attributes-Aware IGF
Existing IGF notions such as SP and EO define the utility of recommending an item to a user only depends on the exposure and interaction numbers. For example, if item i and item i2 are recommended to user U1 and user u2 respectively, then both i and iz have the same utility when ((1, i1) = Y (w2,,2) i2). However, they overlook the social attributes of users. Considering that the user social network plays crucial role in click or conversion behaviors in real-world recommendation scenarios [27]. recommending to users with distinct social attributes may lead to diverse item utilities.
To bridge this gap, we propose social attribute-aware IGF metrics as the extension of previously widely used SP and EO notions. Denote the neighbors (such as friends or followers) of user u as No. for each user v E Nu. let (i) > O be the utility of item i gained from user v via the social influence of user u, when the item recommended the user u. Therefore, for positive rate-based metrics and confusion basrix metrics, the following quantities are required to be similar
NR (g = 9a) Encu EIEZ Go. (1)
()) ( EnCN, Ro(()
For all a= 1, A,
Eveu ErEr Gg. (2)
NR (g- 9a. y/ =) Eueu Eiez Cg. (1) (u, i) 8 (u, EvEN. Ro(i)
for all 1, .A.
Ener Eiez Gg. (i) Y (u,
where the sum of utilitics from the social network ΣvEN. Rs are multiplied by the interaction probability (u, to measure the total social utility. Similar to Eq. 4 we then compute the Neighborhood SP and Neighborhood EO by the relative standard deviations
NSP = rsd (NR (g = 91). NR (g = 9A)), NEO rsd (NR (g = 91. = - 1), 1),,.. .R (g -A.y = 1))
(8)
Further Discussion. For the existing and the proposed IGF notions, the former including SP and EO focus on the direct utility obtained through recommendation exposures to users, whereas the latter including SP and EO emphasize the social utility gained from the user social network. Since these metrics emphasize different aspects, optimizing one IGF notion alone does not guarantee the optimality of the other IGF notion. Figures La and Ib illustrate this with toy example: if we solely optimize SP, it does not guarantee the achievement the other IGF notion, i.e., NSP, and vise versa. Since both IGF metrics are important, it is desirable to optimize both SP (EO) and NSP (NEO) simultaneously from the prospective multi-objective optimization, as illustrated in Figure Ic
4
Methodology
4.1
Multi-Objective Optimization Problem Formulation
The optimization objective for training fair recommendation model under IGF notions is to mini- mize both SP (EO) and NSP (NEO), so as to obtain similar direct utility and similar social utility simultaneously. Building upon prior studies [8] 28), we formulate the fair recommendation training task as a multi-objective optimization problem, where each optimization objective corresponds to a pre-defined IGF metric. Without loss of generality, let the number of IGF metrics used optimization objectives be M, then we aim to obtain Pareto optimal solutions among these IGF metrics.
Pareto Dominance. A solution 0 dominates another solution 0g if (x1)) S L, (02), Vi 1.... M and ((0)) (O),,,), ... (O,)) L()2) = (02), (02))
Pareto Optimality. A solution 0 is Pareto optimal solution if 0 is not dominated by any other solutions. The set of the Pareto optimal solutions is called as Pareto optimal set.

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It is now attractive to formulate the trade-off between different IGF metries as optimization problem, then obtain Pareto-optimal solution between these metries. However, due to the well-known accuracy sacrifice for improving fairness [14], directly solving the above problem without considering recommendation accuracy may lead to a significant reduction in recommendation quality. To ensure controllable recommendation accuracy during the optimization process, we introduce an accuracy constraint that penalizes instances with the accuracy loss (e.g., BPR loss) exceeding a pre-defined threshold. Formally, the multi-objective optimization problem is
min [()) - (2)
(O)" s.1. LBPR(O) E
where & is the pre-defined accuracy threshold, and ş should be set exceed the loss of a recommen- dation model trained using only BPR loss to ensure the existence of feasible solutions.
Furthermore, in real-world recommendation scenarios, the types of IGF metries that consider direct and social effects, respectively, may require different proportions of trade-offs. For example, a recommender system designed for social media applications may place more emphasis on the social utility than the direct utility. Therefore, it is meaningful to find flexible Pareto-optimal solutions to the multi-objective optimization problem with varying trade-offs. Following the previous work (8) decompose the optimization problem into N subproblems using a set of pre-defined unit preference vectors 81, .
: SN R and define the N preference regions 521, $12,.... ................................ S2 follows
Qn = [() E R 20) S " L(0), Vj = 1, ,N}.
(10)
where L()) E 22 and only if L(0) forms the smallest acute angle with sn. resulting in the largest inner product 8 (()) among all sf C(0), s L(O).... 8%, C(0). To ensure that the solution (()) obtained from the optimization phase falls within the preference region Pn, we further impose
constraint that penalizes the distance of the obtained solution from this preference region
min (()) = (C), (2 ... (0))
s.t. g = (s) -,)) ( S =j=1.... ,N
(11)
CBP S g.
By letting the preference vectors be uniformly distributed in RN, we can obtain flexible Pareto optimal solutions with varying trade-offs. Each subproblem corresponds to a unique Pareto-optimal solution in specific preference region, which can reflect different attention to the direct and social utilities. Finally, we can select the desired Pareto optimal solution for diverse recommendation scenarios satisfy both the flexible trade-offs and the controllable prediction accuracy.
4.2 Gradient-Based Flexible and Controllable Fair Recommendation Training
Finding the Initial Solution. For more efficient finding solution to the multi-objective problem that falls within the specified preference region, we first find a feasible initial solution that satisfies all the constraints of that preference region. Specifically, for randomly generated initial solution 0,.. we define the set of indices that violate the constraints as (0,) = {i = 1,. ... .N' (,(e,, 2 -e}. where is small value deal with solutions near the boundary. Then we can compute a descending direction d, that reduces all the values of (0,))) E (.()))) by solving the optimization problem
1
(dr, (.)) = arg min a + ト Iaa. s.I. (g, a, E (O.))
(12)
d.oER
The gradient-basee update rule can be expressed as 0 = 0r, + n where 77, denotes the step size, and will stop when a feasible solution is found or the maximum iteration number is reached.
Solving the Subproblem. Given the feasible initial solution d.. we next propose gradient- based learning approach to solve the multi-objective optimization problem in Eq. (II). Specifically, we compute the update direction d, from 0, to 01+1 by solving the following optimization problem
(dz, ar) = arg min a + ||a112
d
2
s.t. VC, a, i= -,...,,,
(13)
(G, < a, jEL(()))
LLBR (0.) d a. if LBPR (0,) 2 g.
5

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The Lagrange function of the above optimization problem is
1 =lld| Σ ai (Vo,
=
(14)
+
Σ
- a) + X ((BP(((.)) E) (Vo, LBPn ( -a).
(EI,
where a; 2 0 2 0, 2 0 are the Lagrange multipliers. By requiring that the derivatives of C [ a, 0i 8g. A) with respect to both d and a be zero, we have the following equations
M
d =
Σ ==1
a; (,0,)) JEI((0.)
E ByVo. - A ICBBRR (0,) 2 V) (0,)
(15)
M
Σ aat 2=1
Σ JEI,(O.)
B [[CBPR()) 2 =1
Next, we compute the minimal value of Eq. (14 by substituting the corresponding terms in Eq. and obtain the dual problem of Eq. (13) max min & (d, a, 0z, B3, A), equals a., d.a
(5
min a.B
Σ
Vo, L.)
Σ 8,Vo, + + [(Crrn V),o, CBrn (0.)
jEL,0,)
M
s.f.
a
Σ (EL,(0.)
3r ICBBRR 2)) =1
(16)
which can be efficiently solved by the gradient-based optimization methods such MGDA 24
Denote the solutions of Eq. (3) and Eq. [6 (d", a²) and (aj, 3j. >*), respectively. To obtain the solution of the dual problem, according to the KKT conditions, we have
af (Ve (.O,) dt aa") 0, i L.....,, M, 8 (Vo.9((0.)" d' - aa) =0, Vj e (et)..
(17)
A II((APR(O.) 2 {) (Vo, 0 -x") = 0, if CAPR(0.) 2 g.
By adding all equations in Eq. 17 together, have a" - dd'2 In this way,
If 0, Pareto optimal, then no other solution in neighborhood can achieve better objective values, and we obtain the solution d' O, indicating that no direction can simultaneously improve all objective values.
If 0, is not Pareto optimal, we have the following conclusions from Eq. 13
vC, < a < <-'dd' 12 (,) d < 5 - < 0, j. L.O,), (LBPR(O,) Td' < < -1dd" < 0, if CBPR( 2 g.
0, i I,
(18)
therefore d' will be descent direction that at least decreases all the IGF losses simultane- ously, as well as the recommendation accuracy loss when LEPR 2 E.
Finally, the model parameters are updated as 0.+1 = 0, + 7/22 where denotes the step size. Remarkably, throughout the optimization procedure, the values of all IGF objectives and the distance between the obtained solution and the preference region decrease, indicating the Pareto optimality within the preference region. Moreover, tackle the problem of nigh-dimensional parameter in the multi-objective optimization, we propose to optimize its dual problem rather than directly solving the primal problem. As result, numbers of parameters (ar, 3,) in the dual problem significantly reduced to be same as the numbers of IGF objectives and constraints, respectively. which greatly increases the scalability the proposed algorithm to the large-scale recommendation datasets. We summarize the whole cradient-based fair recommendation training process in Algorithm I

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Algorithm 1: Social-Aware Flexible Fair Recommendation with Controllable Accuracy (SoFA)
Input:
Boundary threshold accuracy threshold step size 7/r and 1)-
Set the fairness preference vectors {$1, 82:
.8N):
2 for 7 to N do
Randomly initialize the model parameters 0²")
Find the nearest feasible solution 0 from (( for region 22p for 1 0 to do
if LBP (
(0(") S { then
Obtain at, i 1,... M,, and 3y. j l=(6(")) by solving the dual optimization; Compute the update direction
d, = = EE a 0.Th) (.)) - _jEl, 83 o! G, ()
else
Obtain a,, = 1, M, j..j E T.(( and À by solving the dual optimization; Compute the update direction d!m)
10
11
- Ei=1 a; oft L(( E ( 3, 3, [,
AV of Cgrn(0 (O("))
end
Update the model parameters 0 [ 0 + nd!
13
14
end
15
end
Experiments
In this section we aim to answer the following research questions:
RQ1: How does proposed method perform compared with the existing approaches?
RQ2: Do the preference regions in our method lead
flexible Pareto solutions? Does the accuracy constraint result in more accurate recommendations while achieving IGF?
RQ3: How does varying the accuracy thresholds affect the performance of our method?
5.1
Expertiment Setups
Datasets and Pre-processing, The experiments are performed on two benchmark recommendation datasets that include user social attributes and item features:
KuaiRee a short-video recommendation dataset on the video-sharing platform Kuaishou contains interactions between users and videos. In our experiments, we select user clicks spanning 10 consecutive days as the outcome of interest (29) and apply 10-core filtering to eliminate users and items with minimal interactions, which results
P which
pre-processed dataset consisting of 7,010 users, 1,405 items, and 863,819 interactions. For each user, the number of followers of that user is treated as the user social attribute, and we define the social utility derived from the user social attribute the total fans count of that user. As to videos, we use tags to categorize them into six item groups.
Epinions is dataset derived from trust network, comprising users' rating scores for products. Following previous work (10), we only keep the interactions with ratings greater than 3 and also adopt the 10-core filtering setting. Subsequently, 13,682 items, and 215,262 interactions. For each user, the dataset includes their trust relations with other users, while for each product, it specifies its category. We let user's social utility equal the number of trustors, and classify the products into six groups based on their categories.
obtain dataset consisting of 1 11,710 users,
Throughout experiment, randomly split the interactions of each dataset into training set (60%), validation set (20%), and testing set (20%). We use the validation set for tuning pperrpprraeters and the testing data for evaluation the prediction and faimess performance of the trained models.
https:: stttps://wwy, ://www..wwwwww kuaishou.coom

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Table I: Performance comparison using SP and NSP IGF notions, where SoFA is implemented
with five preference regions. The best and second best results are bolded and underlined, respectively.
KuaiRec
Epinions
5@t
SPJ.
NSP4
FISP
deg
N@5t
SPL
NSP
F1SP/ deg
BPRMF
0.2426
0.0966
0.1119
0.1037 19.29
0.0443
0.0252
0.0286
0.0268 48.6"
+ SP Reg
0.2389
0.0062
0.0168
0.0091
69.7
0.0450
0.0140
0.0196
0.0163
54.55
+ NSP Reg
0.2279
0.0366
0.0142
0,0205
21.29
0.0378
0.0224
0.0188
0.0205
+ SP&NSP Reg
0.2369
0.0090
0.0245
0.0132
60.8
0.0448
0.0154
0.0205
0.0176 63.2
+ SP Post
0.2412
0.0388
0.0545
0.0454
54.5%
0.0445
0.0141
0.0196
0.0164 54.29
+ NSP Post
0.23418
0.0844
0.0311
0.0455
20.3
0.0398
0.0212
0.0185
0.0197
41.2"
+ SP&NSP Post
0.2405
0.0817
0.0562
0.0666
34.5P
0.0443
0.0152
0.0207
0.0175
63.7
MOOMTL
0.2229
0.0069
0.0238
0.0107
73.89
0.0446
0.0138
0.0193
0.0161
54.1"
SoFA region
0.2349
0.0296
0.0096
0.0145
18.0P
0.0364
0.0909
0.0294
0,0445
17.9P
SoFA region
0.2376
0.0179
0.0105
0.0133
30.4P
0.0441
0.0326
0.0225
0.0266 34.69
SoFA region 2
0.2329
0.0103
0.0146
0.0121
54.8%
0.0451
0.0153
0.0210
0.0177 53.9
SoFA region.
0.2413
0.0074
0.0194
0.0107
69.19
0.0427
0.0118
0.0177
0,0142 56.39
SoFA region
0.2402
0.0046
0.0227
0.0077
78.5P
0.0185
0.0095
0.0314
0.0146 73.1
Table 2: Performance comparison using EO and NEO as IGF notions, where SoFA is implemented with five preference regions. The best and second best results are bolded and underlined, respectively.
KuaiRec
Epinions
N@
EOL
NEOJ
FIEO + dog
N@5t
EO|
NEO
FIEO| dog
BPRMF
0.2426
0.0189
0.1081
0.0319 79.6"
0.0443
0.1182
0.2059
0.1502 60.1>
EO Reg
0.2340
0.0044
0.1082
0.0085
87.7"
0.0425
0.1126
0.1956
0.1429
60.19
+ NEO Reg
0.2329
0.0147
0.0992
0.0256 81.6"
0.0430
0.1289
0.1557
0.1410 50.4"
+ EO&NEO Reg
0.2346
0.0054
0.1035
0.0102
87.0*
0.0432
0.1136
0.1465
0.1280 52.2*
+ EO Post
0.2371
0.0061
0.1082
0.0116
86.8
0.0437
0.1100
0.1850
0.1379 59.3*
+ NEO Post
0.2280
0.0143
0.0672
0.0236
78.0"
0.0427
0.1274
0.1565
0.1405 50.8"
+ NO& Post
0.2413
0.0133
0.1039
0.0235
82.7
0.0436
0.1131
0.1630
0.1335 55.3*
MOOMTL
0.2332
0.0031
0.1003
0.0061
88.2
0.0444
0.1093
0.1449
0.1246
53.0%
SoFA
region
0.1635
0.1454
0.0557
0.0806
21.0*
0.0224
0.3273
0.1494
0.2051
24.5"
SoFA region
0.2077
0.1135
0.0558
0.0749
26.2"
0.0353
0.1752
0.1394
0.1552 38.5*
SoFA region
0.2254
0.0610
0.0528
0.0566
40.9*
0.0448
0.1094
0.1473
0.1256 53.4"
SoFA rugion
0.2241
0.0284
0.0713
0.0406
68.3"
0.0443
0.1160
0.1604
0.1347 51.1"
SoFA region
0.2352
0.0023
0.0685
0.0045
88.1
0.0447
0.1157
0.1574
0.1334 59.79
Evaluation Protocols. We evaluate the recommendation accuracy with NDCG@5 30 For
evaluating IGF, we report both the previous fairness metrics and social attribute-aware metrics, where lower value indicates fairer performance. We study two settings with (SP, NSP) and (EO, NEO) as the IGF objectives, respectively. Under each setting, the overall faimesss is assessed using the harmonic-mean of the two IGF metrics denoted as FISP. In addtion, to quantify the trade- offs between the two IGF metrics, we calculate the angles formed by these metrics via deg = arctan(NSP /SP), where a lower angle degree signifies a greater emphasis on the social utility.
Hyper- Parea--ar Settings. For all compared methods, we use pre-trained BPRMF [9] as the backbone with fixed optimal batch size and regularization coefficient, then fine-tune the model by using the baselines methods for achieving IGF notions. For the proposed SoFA, we set N = 5 as the number of preference vectors that equally divide the first quadrant, and tune the learning rate for finding the initial solution within (0.3Ir, Ir. 3lr}. where Ir denotes the learning rate for the pre-trained BPRMF This optimization step stops once a feasible solution found. The learning rate for all methods is searched within (0.03lr, 0.1,r, 0.3lr, Ir. 3lr, 10lr), and the coefficients of IGF terms for regularization-bal based and post-processing baselines are searched within (0.1, 0.2, 0.5, 1, 2, 5). The carly stopping strategy is employed when the FISP FIEO value does not decrease over 5 epochs.
8

---

0.245
A (1)
BPRMF
SoFA
SoFA (2)
Both Post SP Post
SoFA x
NSP Reg
Rep
0.240
4pp
SoFA
SoFA (3) SOFAA
SP Reg
loggNSP
NSP Post
Both Reg MOOMTL
0.235
NSP Post
Both Reg
N@5
SoFA
SoFA (2)
Both Post
0.230
NSF Reg
MOOMTL
BPRMF
0.220
4
5
7
3
5
6
-log,5P
-log2F1SP
(a) SP and NSP trade-off
(b) FISP and NDCG@5 trade-off
The trade-offs KuaiRec between (a) IGF metrics, i.e,, SP and NSP, and (b) overall fairness and accuracy. i.e., FISP and NDCG, where yellow lines refer to the results when only optimizing one IGF metric, and scatters located on the upper right indicate better overall performance.
Figure 2:
Table 3: Ablation studies of SoFA on the accuracy constraint, IGF objectives, and preference region.
KuaiRec
Epinions
N@5t
SPL
NSPL
FISP 4 dog
N@5t
SP
NSP
FISP
| deg
SoFA region
0.2349
0.0296
0.0096
0.0145
18.0"
0.0364
0.0909
0.0294
0.0445
17.9*
w/o con
0.2181
0.0415
0.0124
0.0191
16.6P
0.0339
0.0814
0.0260
0.0395
17.79
SoFA region
0,2376
0.0179
0.0105
0.0133
30.4
0.0441
0.0326
0.0225
0.0266
34.6*
w/o con
0.2254
0.0211
0.0121
0.0154
29.8
0.0429
0.0371
0.0267
0.0311
35.89
SoFA region 2
0,2329
0.0103
0.0146
0.0121
54.8P
0.0451
0.0153
0.0210
0.0177
53.
w/o con
0.2117
0.0085
0.0131
0.0103
57.09
0.0445
0.0163
0.0224
0.0189
53.99
SoFA region 0,2413
0.0074
0.0194
0.0107
69.1
0.0427
0.0118
0.0177
0.0142
56.39
w/o con 0.2212
0.0077
0.0216
0.0113
70.49
0.0417
0.0131
0.0222
0.0165
59.49
SoFA 4 0.2402
0.0046
0.0227
0.0077
78.5*
0.0185
0.0095
0.0314
0.0146
73.19
w/o con
0.2193
0.0069
0.0256
0.0109
74.9"
0.0169
0.0093
0.0313
0.0144
73.49
w/o SP 0.2220
0.0206
0.0064
0.0098
17.4"
0.0365
0.0216
0.0147
0.01
3-1.39
w/o NSP 0.2415
0.0050
0.0173
0.0077
74.0"
0.0447
0.0148
0.0200
0.01 70 53.5
w/o region 0.2412
0.0046
0.0193
0.0074
76.79
0.0447
0.0141
0.0197
0.0164
54.49
5.2 Performance Comparison (RQ1)
We compare our proposed SoFA with the vanilla BPRMF 9 and several baseline methods to achieve recommendation fairness. These baselines include: (1) Regularization based method (31,, which incorporates IGF metrics as regularization terms into the BPR loss. (2) Post- pess-processing method [32
which reconstructs the recommendation results while imposing fairness objectives as constraints. (3) Multi-objective optimization- -based method (28), which optimizes the formulated multi-objective
problem without the preference regions and recommendation accuracy constraint. We adopt three versions of regularization-based methods and post-processing methods, which considers only direct utility (SP or EO), only social utility (NSP or NEO), and both utilitics, respectively.
Tables I and 2 show the overall performance of compared methods under the (SP, NSP) and (EO, NEO) settings, respectively, from which we have the following observations: (1) all cases, SoFA outperforms other baselines in terms of accuracy and fairness, which validates its effectiveness in fairly recommending with accuracy guarantee. (2) SoFA can effectively find solutions in different preference regions, showing the ability to accommodate customized trade-off between the direct utility and social utility as the IGF metrics. Figure 2a visualizes the trade-off between SP and NSP, showing that SoFA is able to find pareto optimal solutions between the IGF metrics. Figure 2b suggests that FISP and NDCG do not always exhibit conflicting trade-off, meaning that enhancing fairness does not necessarily sacrifice recommendation accuracy in certain scenarios.

---

x1.2
None
x1.0
x1.1
x1.2
Nore
0.25
0.020
0.24
N@s
0.23
F1SP
0.015
0.22
0.010
0.21
0.15
0.005
(0".18") [18",36") (36",54") [54".72") [72",90"]
[0'.18") (18",36") 55") [54".72") [72" ,90"]
Preference Region's Range
Preference Region's Range
(a) NDCG@5
(b) FISP
Figure 3: Effects of varying accuracy thresholds in the optimization on KuaiRec with 100 repeats.
5.3 In-depth Analysis
Ablation Study (RQ2). We conduct the following ablations to evaluate the effectiveness of specific designs in SoFA: (I) w/o con, which trains the model without the recommendation accuracy constraint. (2) w/o region, which trains the model without specifying the preference region. (3) w/o SP, which trains the model without the SP fairness loss, thus does not require the preference region specification. (4) w/o NSP, similar w/o SP but trains the model without the NSP fairness loss. Table 3 shows the performance of SoFA and its ablated versions, we find that training the model without the accuracy constraint encounters significant drop in recommendation accuracy compared to SoFA, indicating the effectiveness of the proposed accuracy constraint. In addition, removing the specification of the preference region may hurt the performance in terms of accuracy and fairness, because the preference region do not directly contribute to the recommendation accuracy and overall fairness. However, fails obtain recommendation model with flexibility to trade-off these IGF metrics.
Effects of Accuracy Requirement (RQ3), To further investigate the effect of recommendation accuracy constraint, we evaluate SoFA with relaxed constraints by increasing the threshold & in Eq. In particular, we compare the default choice the accuracy threshold with 1.1 times and 1.2 times of that value, as well the optimization without the recommendation accuracy constraint. We conduct 100 runs for each optimization process on KuaiRec with varying preference regions. Figure 3 shows the accuracy and fairness performance, and we have observations as below: (1) NDCG has a clear decrease trend as the threshold increases, which further reveals that constraining the recommendation loss can control the accuracy of the obtained solution. (2) FISP improves as the threshold decreases in most regions, which indicates that the accuracy constraint may also benefit the fairness. Therefore, we suggest to use the original BPRMF loss as the accuracy threshold in practice.
6 Conclusion
This study addresses a new problem in IGF motivated by the effect of user social influence on item utility. First, we propose two IGF notions, namely NSP and NEO, as extensions the existing IGF notions that only considers the direct utility of item exposures. Next, we formulate multi-object objectvv optimization problem with pre-defined preference regions ensure the flexibility of the trade-off between these IGF metrics. Then, we incorporate recommendation accuracy constraint to control the accuracy sacrifice for satisfying the fairness requirements. We further propose an algorithm to solve the optimization problem and theoretically demonstrate its Pareto optimality. Extensive experiments on two real-worke datasets validate the effectiveness of our method. One interesting future research direction is generalize the user social influence studies in this paper ranking-based IGF settings.
Acknowledgement
This work is supported by the National Key Research and Development Program of China (No. 2022YFB3 and the National Natural Science Foundation of China (No. 12301370).
10

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12


Reviews:
[{"review_id": "MxFcUlmHXt", "reviewer": "Reviewer_pts6", "summary": "This paper introduces a new problem of fairness in recommendation tasks, specifically considering the social attribute of users and its influence on item exposures. The paper proposes social attribute-aware fairness metrics and formulates a multi-objective optimization problem to train recommender models with customizable trade-offs between direct and social utilities. The paper presents a new optimization algorithm and provides theoretical guarantees. Experimental results on real-world datasets demonstrate the effectiveness of the proposed approach.", "questions": "My concerns involves clarity, expeirments, implementations, etc.. Please refer to the above comments. ", "limitations": "N/A", "rating": 2, "confidence": 5, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "(1) The paper addresses an important and timely topic of fairness in recommendation systems, taking into account the social attribute of users.\n(2) The introduction of social attribute-aware fairness metrics provides a more comprehensive and holistic view of fairness in recommendation tasks.\n(3) The formulation of a multi-objective optimization problem allows for flexible customization of the trade-off between direct and social utilities, providing a practical solution for real-world scenarios.", "weaknesses": "(1) The paper lacks clarity in the presentation of the optimization algorithm and its theoretical guarantee. More detailed explanations and proofs would be helpful.\n(2) The evaluation section could be improved with a more comprehensive comparison with existing baselines in the field of fairness-aware recommendation systems.\n(3) The implementation details are not enough.\n(4) The writing should be improved.\n(5) Please discuss more about the application scenario of the proposed method.\n(6) Please use more datasets to provide more solid results.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank you for the helpful suggestions. **As suggested by the reviewer, we have added extensive discussions and experiments to address all your concerns.** Below, we hope to address your concerns and questions to improve the clarity and quality of our paper.\n\n### **Methodology**\n\n> **W1:** The paper lacks clarity in the presentation of the optimization algorithm and its theoretical guarantee. More detailed explanations and proofs would be helpful.\n\n**Response**: Setting other optimization objectives makes it difficult to theoretically achieve Pareto optimality, and the proposed method has strict theoretical guarantees. Please kindly refer to lines 185-190 in our manuscript.\n\n### **Novelty**\n\n**Response**: We kindly remind the reviewer that the novelties of this paper are:\n- (a) the proposed social-attribute aware IGF metrics (namely NSP and NEO) corresponding to SP and equal opportunity (EO), respectively, to take into account the direct and social attributes of the users; \n- (b) the proposed Pareto optimization, compared with [1], has more flexible and controllable (via pre-specified preference regions) trade-offs between SP and NSP (as well as between EO and NEO); \n- (c) theoretically demonstrates that the proposed optimization can achieve the Pareto optimal solution for SP and NSP (as well as for EO and NEO) while guaranteeing the least accuracy of the learned recommendation model.\n\n### **Experiments**\n> **W2:** The evaluation section could be improved with a more comprehensive comparison with existing baselines in the field of fairness-aware recommendation systems.\n\n> **W3:** The implementation details are not enough.\n\n> **W5:** Please discuss more about the application scenario of the proposed method.\n\n> **W6:** Please use more datasets to provide more solid results.\n\n**Response**: Thanks for your comments.\n\n-\tDue to the page limits, we **postpone the detailed dataset descriptions in Appendix B1 in supplementary material,** including their origination, processing procedures, statistics, grouping method and social attributes.\n\n-\t**As suggested by the reviewer, we add extensive experiments by taking NeuMF and NGCF as backbone model, respectively.** Moreover, we **set varying $R_v$ with different users, items, and user-item pairs, respectively, to validate the effectiveness of our method.** Please kindly refer to the attachment PDF for more details. From the tables in the attached pdf, we can observe that our method can always achieve the best fairness performance (i.e. minimum SP/NSP/F1SP/EO/NEO/F1EO values) and diverse trade-off between two sets of IGF metrics compared to other baselines. Additionally, in EO&NEO cases, our method may not obtain the best NDCG value apart from the basemodel, and we attribute this to the fairness-utility trade-off phenemenon; despite from that, our method can always get optimal NDCG values in SP&NSP settings.\n\n-\tMore discussion on Fig. 2: the figures in Fig. 2 is divided into four regions by two reference lines, which represents the corresponding metric value of x/y-axis obtained by single-objective optimization methods. More specifically, in the 1st and 3rd subfigure, the hierarchical line refers to the -log2NSP value of NSP Reg baseline, and the vertical line refers to the -log2SP value of SP Reg baseline; in the 2nd and 4th subfigure, we take the NDCG and -log2F1SP value of SP Reg baseline for reference. As for the divided four regions, the solutions in upper right (lower left) region can achieve better (worse) performance than both two reference lines (i.e. Pareto dominance), and the solutions in upper right / upper left / lower right region are regarded as Pareto optimal solutions.\n\n### **Presentation**\n> **W4:** The writing should be improved.\n\n**Response**: Thank you for your comments. We apologize for the lack of clarity. We have made careful corrections throughout our manuscript.\n\n***\n\n**We hope the above discussion will fully address your concerns about our work, and we would really appreciate it if you could be generous in raising your score.** We look forward to your insightful and constructive responses to further help us improve the quality of our work. Thank you!\n\n"}, {"review_id": "KEAIZ2Wtyp", "reviewer": "Reviewer_cJkK", "summary": "This paper aims to solve the Item-side Group Fairness (IGF) issue in Recommender Systems (RSs). The paper claims that existing IGF notions only focus on the direct utility of item exposures while ignore the influence from the social attributes of users. To tackle this issue, the paper proposes social attribute-aware IGF metrics and utilizes a multi-objective optimization method to enhance the fairness of a given recommendation model. Experiments on two public datasets have been conducted to prove the efficiency of the proposed method.", "questions": "1. Why this paper chooses BRPMF to conduct your experiments rather than some novel deep-learning-based methods like NeuMF and NGCF?\n2. Why optimizing the model with only SP can achieve the best NSP fairness?\n3. Why you didn’t conduct an experiment of the effect of the value of $R_v$?\n------------------------------\nDear authors,\nThanks for your response. Some of my concerns have been addressed, and I would like to improve my rating.", "limitations": "N/A", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "The strengths of this paper can be summarized into several aspects:\n1. The paper addresses an important research area in machine learning, which is the fairness of recommendation systems. The inclusion of social attributes in the proposed IGF model adds an interesting dimension to this field.\n\n2. The experimental results demonstrate the efficiency of the proposed method. The performance of the proposed method outperforms other baselines across all datasets, which highlights its effectiveness.\n\n3. The utilization of a multi-objective optimization method to solve the problem presented in the paper is a convincing approach. This method ensures that the accuracy of the recommendation model is maintained while enhancing the fairness aspect.", "weaknesses": "The weaknesses of this paper can be summarized into several aspects:\n\nIdea and technique\n1. The effect of social attributes on IGF is not clear. The authors should provide more empirical studies using the given datasets and conduct further analysis to describe the relationship between social attributes and IGF. A toy example in Figure 1 is insufficient to help readers understand this issue. For a fairness problem, it is crucial to clearly describe the problem and demonstrate its importance.\n2. While utilizing a multi-objective optimization method (e.g., Pareto optimization) is convincing, it is not novel enough. Similar methods have been widely used in recommender systems, like [1].\n\nPresentation\n1. I highly recommend that the authors give a proper name to their method, which would make it more convenient for referencing. (This is not a reason for my rejection).\n2. Some mathematical notations are not clear in this paper, making it hard to follow. For example, $G_{g_a}(i)$ in line 82 should reflect its relationship to $u$. Besides, $R_v$ in line 117 should reflect its relationship to $u$ and $i$.\n\nExperiment\n1. Although BPRMF is a classical recommendation method, it is an outdated recommendation algorithm compared to deep-learning-based methods used in modern recommender systems. Therefore, mitigating fairness in BRPMF may have limited impact in today's systems. Exploring the fairness issue using popular deep-learning algorithms like NeuMF[2] and NGCF[3] may be more effective to evaluate the proposed method.\n2. The value of $R_v$ is important for the proposed method. The authors should conduct experiments with different values of this hyperparameter to prove why they set the default value to 1.\n3. In the ablation study, when optimizing the model with only SP (i.e., w/o SP), the model achieves the best NSP fairness. The paper should analyze the reason for this.\n\n[1] Hao Q, Xu Q, Yang Z, et al. Pareto optimality for fairness-constrained collaborative filtering[C]//Proceedings of the 29th ACM International Conference on Multimedia. 2021: 5619-5627.\n[2] He X, Liao L, Zhang H, et al. Neural collaborative filtering[C]//Proceedings of the 26th international conference on world wide web. 2017: 173-182.\n[3] Wang X, He X, Wang M, et al. Neural graph collaborative filtering[C]//Proceedings of the 42nd international ACM SIGIR conference on Research and development in Information Retrieval. 2019: 165-174.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank you for the helpful suggestions. **As suggested by the reviewer, we have added extensive experiments to address all your concerns.** Below, we hope to address your concerns and questions to improve the clarity and quality of our paper.\n\n### **Idea and technique**\n> **W1(a):** The effect of social attributes on IGF is not clear. The authors should provide more empirical studies using the given datasets and conduct further analysis to describe the relationship between social attributes and IGF. A toy example in Figure 1 is insufficient to help readers understand this issue. For a fairness problem, it is crucial to clearly describe the problem and demonstrate its importance.\n\n**Response to W1(a):** We thank the reviewer for the helpful suggestions and apologize for the lack of clarity. This paper argues that previous studies on item-side group fairness (IGF) have **lacked consideration of user-side utility** that **depends on a user's social attributes.** The core intuition is that, **for a given item (in an item-group), recommending it to a user with \"richer (more active)\" social attributes will result in greater utility in practice, due to the fact that the user $u$'s interaction (e.g., clicks or purchases) may by affected by its neighbors $\\mathcal{N}_u$.** This is also known as user conformity bias in previous debiased recommendation studies [Zheng et al. \"Disentangling user interest and conformity for recommendation with causal embedding.\" WWW 2021].\n\nTo tackle the above problem, the fairness metric studied in this paper considers both the exposure chance of the items and the social attributes of the corresponding recommended users, and is formalized as a multi-objective optimization problem. Taking the widely-studied statistical parity (SP) in IGF as an example, we not only want item-group A and item-group B to have the same exposure rates, but also want the users to whom item-group A is recommended to have similar social attributes as the users to whom item group B is recommended to. We hope the above clarification provides more understanding of the motivation for our work.\n\n> **W1(b):** \nWhile utilizing a multi-objective optimization method (e.g., Pareto optimization) is convincing, it is not novel enough. Similar methods have been widely used in recommender systems, like [1].\n\n**Response to W1(b):** The reviewer raises an interesting concern. We **agree** that using a multi-objective optimization (e.g., Pareto optimization) is not novel by itself. However, the novelties of this paper are:\n- (a) the proposed social-attribute aware IGF metrics (namely NSP and NEO) corresponding to SP and equal opportunity (EO), respectively, to take into account the direct and social attributes of the users; \n- (b) the proposed Pareto optimization, compared with [1], has more flexible and controllable (via pre-specified preference regions) trade-offs between SP and NSP (as well as between EO and NEO); \n- (c) theoretically demonstrates that the proposed optimization can achieve the Pareto optimal solution for SP and NSP (as well as for EO and NEO) while guaranteeing the least accuracy of the learned recommendation model.\n\n### **Presentation**\n\n> **W2:** Some mathematical notations are not clear in this paper, making it hard to follow. For example, $G_{g_a}(i)$ in line 82 should reflect its relationship to $u$. Besides, $R_v$ in line 117 should reflect its relationship to $u$ and $i$.\n\n**Response to W2:** We thank the reviewers for the useful comments. **Yes, $R_v$ in line 117 should be $R_v(u, i)$ instead of $R_v(u)$.** However, **$G_{g_a}(i)$ in line 82 is the group indicator of item $i$,** i.e., equals to 1 if item $i$ belongs to item-group $g_a$, thus **should not** relies on $u$.\n\n\n### **Experiment**\n> **W3(a):** Although BPRMF is a classical recommendation method, .... Exploring the fairness issue using popular deep-learning algorithms like NeuMF[2] and NGCF[3] may be more effective to evaluate the proposed method.\n\n> **Q1:** Why this paper chooses BRPMF to conduct your experiments rather than some novel deep-learning-based methods like NeuMF and NGCF?\n\n**Response to W3(a) and Q1:** Thanks for your helpful suggestion. **As suggested by the reviewer, we add extensive experiments by taking NeuMF and NGCF as backbones, respectively, to validate the effectiveness of our proposal.** Please kindly refer to the attachment PDF for more details.\n\n> **W3(b):** In the ablation study, when optimizing the model with only SP (i.e., w/o SP), the model achieves the best NSP fairness. The paper should analyze the reason for this.\n\n> **Q2:** Why optimizing the model with only SP can achieve the best NSP fairness?\n\n**Response to W3(b) and Q2:** We thank the reviewer for pointing out this issue. **We believe that there is a misunderstanding here due to our typo: \"w/o\" in this paper means \"without\", not \"with only\".** Therefore, the model that considers only NSP (i.e., w/o SP) achieves the optimal NSP fairness.\n\n> **W3(c):** The value of $R_v$ is important for the proposed method. The authors should conduct experiments with different values of this hyperparameter to prove why they set the default value to 1.\n\n> **Q3:** Why you didn’t conduct an experiment of the effect of the value of $R_v$?\n\n**Response to W3(c) and Q3:** We agree with you and **have added the experiments by set varying $R_v$ with different users, items, and user-item pairs, respectively.** Specifically, we set $R_v(u)$ equals number of items that user u has interacted with, $R_v(i)$ equals number of users that item i has interacted with, and $R_v(u, i)=R_v(u)*R_v(i)$, respectively. Please kindly refer to the attachment PDF for more details.\n\n***\n**We hope the above discussion will fully address your concerns about our work, and we would really appreciate it if you could be generous in raising your score.** We look forward to your insightful and constructive responses to further help us improve the quality of our work. Thank you!"}, {"review_id": "QoQBl9m9Zv", "reviewer": "Reviewer_ZQVW", "summary": "This paper considered both direct and social utilities on the Item-side group fairness (IGF). The authors proposed a new flexible and controllable optimization approach to trade-off the utilities while ensuring accuracy. Firstly, they proposed two social attribute-aware IGF metrics, NSP and NEO by leveraging user’s social attributes. They then formulated a new multi-objective optimization (MOP) problem for training recommendation models with flexibility that incorporated a recommendation loss constraint into the MOP to maintain control over the optimization process on the two sets of IGF metrics. Additionally, they developed a new optimization algorithm to solve the MOP and achieve restricted Pareto optimality. Finally, they conducted extensive experiments on multiple real-world datasets to demonstrate the effectiveness of their proposed method. Please refer to the previous section for the strengths and weaknesses of this work. ", "questions": "\n1)\tHow is the number N of users aggregated in NSP and NEO determined?\n2)\tWhether the same inference can be achieved if other optimization objectives are used?\n3)\tWhether the user's social attributes themselves may contain certain sensitive attributes that cause unfairness in the group?\n", "limitations": "The authors argue that the limitation of the work in this paper is that it does not consider the ranking-based IGF metrics, they should careful thought needs to be given to what the two metrics proposed can do for their future work and how to build and solve the new MOP problem.", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "1)\tThis paper focused on the Item-group fairness and considered the social utility by utilizing user’s social attributes, which has certain research value.\n2)\tThis paper expanded the previous fairness metrics to proposed two new social attribute-aware IGF metrics that considered the the distribution of neighbors of users.\n3)\tThis paper formulated a new MOP for training recommendation models to achieve controllable optimization and flexible optimization.\n4)\tThis paper developed a new optimization algorithm and provide its theoretical guarantee of approaching restricted Pareto optimality to make reasoning process more rigorous and clear.\n5)\tThis paper conducted extensive experiments over on real-world datasets to demonstrate the effectiveness of the proposed method.\n", "weaknesses": "1) In the introduction:\nThe introduction of relevant work is not detailed enough, mainly using legends to illustrate viewpoints and put forward new fairness indicators, but the illustration of legends is not very intuitive.\n\n2) In the Experiments:\na. The datasets are not described.\nb. Some other relevant fairness indicators should also be compared.\nc. The analysis of the results of the model is not very detailed, and the proposed SP&NSP does not achieve a good result.\nd. What do the four regions in Figure 2 refer to? Suggested description in conjunction with the datasets.\n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for your thoughtful and comprehensive feedback on our paper. With your helpful comments, we have revised the **Introduction** and **Experiments** Sections with the aim of presenting the relevant work in a more systematic and clear manner, as well as adding missing experimental details.\n\n### **Introduction**\n\n> W1: More detailed introduction of relevant work.\n\n**Response to W1:** We thank the reviewer for the useful comment, and **we'll include the following paragraph to the related work section in our revised version of paper, regarding the previous studies of fairness in recommendation.**\n\n\"Recently, there have been growing attention on fairness issue in recommender systems [1,2]. The taxonomy of fairness notions in recommendation can be categorized from different aspects [3,4]. For example, as for different subjects, existing works usually eliminate unfairness in recommendation for user-side [5], item-side [13] and multi-side [6]; as for different granularities, the fairness  notions can be categorized into group fairness [5] and individual fairness [7]. In this work, we focus on item-side group fairness [8,9,10], which requires that different item groups should be treated similarly by the recommender system. Previous works on IGF usually pursues the Statistical Parity and Equal Opportunity of different item groups [11,12,13]. However, they overlook the social utility of item exposures. As users with varying social attributes may bring impact on their friends, each recommendation to different users may result in varying utilities. In this work, we introduce social attribute-aware IGF metrics, and further investigate on solving the trade-off between two sets of IGF metrics under controllable accuracy.\"\n\n### **Experiments**\n\n> W2(a): Description of datasets.\n\n**Response to W2(a):** Due to the page limits, we **postpone the detailed dataset descriptions in Appendix B1 in supplementary material,** including their origination, processing procedures, statistics, grouping method and social attributes.\n\n> W2(b): Other relevant fairness indicators; More detailed result analysis.\n\n**Response to W2(b):** The reviewer raises an interesting concern. We add extensive experiments by taking NeuMF and NGCF as backbone model, respectively. Moreover, we set varying $R_v$ with different users, items, and user-item pairs, respectively, to validate the effectiveness of our method. Please kindly refer to the attachment PDF for more details.\n\n> W2(c): The proposed SP&NSP does not achieve a good result.\n\n**Response to W2(c):** We thank the reviewer for pointing out this issue. We believe that there is a misunderstanding. **In fact, \"SP&NSP Reg (Post)\" is one of our compared baselines,** which imposes both SP and NSP as regularization (post reconstruction) terms in the regularization-based (post-processing) method. In Table 1, all of our proposed method achieved best performance w.r.t. different fairness metrics.\n\n> W2(d): What do the four regions in Figure 2 refer to?\n\n**Response to W2(d):** As the reviewer pointed out, each subfigure of Figure 2 is divided into four regions by two reference lines, which represents the corresponding metric value of x/y-axis obtained by single-objective optimization methods. More specifically, in the 1st and 3rd subfigure, the hierarchical line refers to the -log2NSP value of NSP Reg baseline, and the vertical line refers to the -log2SP value of SP Reg baseline; in the 2nd and 4th subfigure, we take the NDCG and -log2F1SP value of SP Reg baseline for reference. As for the divided four regions, the solutions in upper right (lower left) region can achieve better (worse) performance than both two reference lines (i.e. Pareto dominance), and the solutions in upper right / upper left / lower right region are regarded as Pareto optimal solutions.\n\n### **Questions**\n\n> Q1: Number of aggregated users in NSP/NEO\n\n**Response to Q1:** In our work, the number of aggregated users in NSP/NEO equals to $|\\mathcal{N}_u|$, i.e., the number of the neighbors of user $u$.\n\n> Q2: Other optimization objectives\n\n**Response to Q2:** Setting other optimization objectives makes it difficult to theoretically achieve Pareto optimality, and the proposed method has strict theoretical guarantees. Please kindly refer to lines 185-190 in our manuscript.\n\n> Q3: user social attributes\n\n**Response to Q3:** This paper argues that previous studies on item-side group fairness (IGF) have lacked consideration of user-side utility that depends on a user's social attributes, rather than from the sensitive attributes prospective. And we will leave the problem of \"the user's social attributes themselves may contain certain sensitive attributes that cause unfairness in the group\" in our further work.\n\n\n***\n**References**\n\n[1] Rectifying Unfairness in Recommendation Feedback Loop. SIGIR 2023.\n\n[2] Scoping Fairness Objectives and Identifying Fairness Metrics for Recommender Systems: The Practitioners’ Perspective. WWW 2023.\n\n[3] Fairness in Recommendation: A Survey. Arxiv 2022.\n\n[4] A Survey on the Fairness of Recommender Systems. TOIS 2023.\n\n[5] Improving Recommendation Fairness via Data Augmentation. WWW 2023.\n\n[6] Joint Multisided Exposure Fairness for Recommendation. SIGIR 2022.\n\n[7] FairGAN: GANs-based Fairness-aware Learning for Recommendations with Implicit Feedback. WWW 2022.\n\n[8] Fairness in Recommendation Ranking Through Pairwise Comparisons. KDD 2019.\n\n[9] Fairness-Aware Ranking in Search & Recommendation Systems With Application to LinkedIn Talent Search. KDD 2019.\n\n[10] Towards Long-term Fairness in Recommendation. WSDM 2021.\n\n[11] Towards a Fair Marketplace: Counterfactual Evaluation of the Trade-Off Between Relevance, Fairness & Satisfaction in Recommendation Systems. CIKM 2018.\n\n[12] Achieving Fairness via Post-processing in Web-Scale Recommender Systems. FACCT 2022.\n\n[13] ProFairRec: Provider Fairness-aware News Recommendation. SIGIR 2022."}, {"review_id": "ylRnl5kPZK", "reviewer": "Reviewer_PYwN", "summary": "Item-side group fairness (IGF) is crucial in recommendation tasks. Existing fairness notions focus on direct utility of item exposures but overlook the social utility, such as the influence of users' social attributes on exposed items. This paper introduces social attribute-aware IGF metrics and proposes a new IGF problem considering both direct and social utilities. To address the trade-off between these utilities, a new multi-objective optimization problem is formulated for training recommender models, allowing customizable trade-offs while maintaining controllable accuracy. A new optimization algorithm is developed with a theoretical guarantee of approaching restricted Pareto optimality. Experiments on real-world datasets confirm the effectiveness of this flexible and controllable approach.", "questions": "N/A", "limitations": "The authors have discussed the limitation.", "rating": 7, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "Introducing social utility into group fairness if a reasonable assumption and this work proposed a viable solution with two new metrics. The experiments are thorough and detailed. This work is complete and sound.", "weaknesses": "1. Matrix factorization is not the mainstream choice for recommendation in practice. Tree model and deep model are the hot choice. Choosing them as backbone may further improve the impacts of this work.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "> **W1:** Matrix factorization is not the mainstream choice for recommendation in practice. Tree model and deep model are the hot choice. Choosing them as backbone may further improve the impacts of this work.\n\n**Response to W1:** Thanks for your helpful suggestion. **As suggested by the reviewer, we add extensive experiments by taking NeuMF and NGCF as backbones, respectively, to validate the effectiveness of our proposal** in below, to address your concerns of our work.\n\n| SP&NSP          | NDCG          | SP            | NSP           | F1SP          | deg  | EO&NEO          | NDCG          | EO            | NEO           | F1EO          | deg  |\n| --------------- | ------------- | ------------- | ------------- | ------------- | ---- | --------------- | ------------- | ------------- | ------------- | ------------- | ---- |\n| **NeuMF**       | 0.2220        | 0.2013        | 0.2464        | 0.2216        | 50.8 | **NeuMF**       | **0.2220**    | 0.0291        | 0.1006        | 0.0451        | 73.9 |\n| + SP Reg        | $\\underline{0.2260}$ | 0.0157        | 0.0473        | 0.0235        | 71.7 | + EO Reg        | 0.2125        | 0.0034        | 0.1077        | 0.0066        | 88.2 |\n| + NSP Reg       | 0.2223        | 0.0229        | 0.0228        | 0.0228        | 44.9 | + NEO Reg       | 0.2191        | 0.0281        | $\\underline{0.0363}$ | 0.0317        | 52.2 |\n| + SP&NSP Reg    | 0.2256        | 0.0165        | 0.0620        | 0.0261        | 75.1 | + EO&NEO Reg    | 0.2191        | 0.0053        | 0.1034        | 0.0100        | 87.1 |\n| + SP Post       | 0.2146        | 0.0151        | 0.0631        | 0.0243        | 76.6 | + EO Post       | 0.2183        | 0.0042        | 0.1073        | 0.0082        | 87.7 |\n| + NSP Post      | 0.2138        | 0.0686        | 0.0421        | 0.0522        | 31.5 | + NEO Post      | 0.2142        | 0.0185        | 0.0384        | 0.0250        | 64.3 |\n| + SP&NSP Post   | 0.2161        | 0.0187        | 0.0433        | 0.0262        | 66.6 | + EO&NEO Post   | 0.2168        | 0.0044        | 0.0721        | 0.0084        | 86.5 |\n| MOOMTL          | 0.1695        | 0.0177        | 0.0611        | 0.0274        | 73.9 | MOOMTL          | 0.2113        | $\\underline{0.0034}$ | 0.1065        | $\\underline{0.0065}$ | 88.2 |\n| Ours (region 0) | 0.1529        | 0.1064        | **0.0166**    | 0.0287        | 8.9  | Ours (region 0) | 0.1015        | 0.1130        | **0.0361**    | 0.0547        | 17.7 |\n| Ours (region 1) | 0.2237        | 0.0305        | $\\underline{0.0171}$ | 0.0219        | 29.2 | Ours (region 1) | 0.1967        | 0.0830        | 0.0471        | 0.0601        | 29.6 |\n| Ours (region 2) | 0.2211        | 0.0540        | 0.0659        | 0.0594        | 50.7 | Ours (region 2) | 0.1917        | 0.1228        | 0.0926        | 0.1056        | 37.0 |\n| Ours (region 3) | 0.2136        | **0.0106**    | 0.0281        | **0.0153**    | 69.4 | Ours (region 3) | 0.2003        | 0.0744        | 0.1136        | 0.0899        | 56.8 |\n| Ours (region 4) | **0.2263**    | $\\underline{0.0139}$ | 0.0484        | $\\underline{0.0216}$ | 73.9 | Ours (region 4) | $\\underline{0.2201}$ | **0.0017**    | 0.0941        | **0.0033**    | 89.0 |\n\n| SP&NSP          | NDCG          | SP            | NSP           | F1SP          | deg  | EO&NEO          | NDCG          | EO            | NEO           | F1EO          | deg  |\n| --------------- | ------------- | ------------- | ------------- | ------------- | ---- | --------------- | ------------- | ------------- | ------------- | ------------- | ---- |\n| **NGCF**        | 0.2389        | 0.1164        | 0.1356        | 0.1253        | 49.4 | **NGCF**        | **0.2389**    | 0.0210        | 0.1045        | 0.0349        | 78.7 |\n| + SP Reg        | 0.2372        | 0.0034        | 0.0202        | 0.0058        | 80.5 | + EO Reg        | 0.2351        | 0.0019        | 0.1110        | 0.0037        | 89.0 |\n| + NSP Reg       | 0.2318        | 0.0109        | 0.0114        | 0.0111        | 46.3 | + NEO Reg       | 0.2329        | 0.0092        | 0.0666        | 0.0161        | 82.2 |\n| + SP&NSP Reg    | 0.2392        | 0.0044        | 0.0185        | 0.0072        | 76.5 | + EO&NEO Reg    | 0.2338        | 0.0022        | 0.0763        | 0.0043        | 88.4 |\n| + SP Post       | 0.2378        | 0.0048        | 0.0253        | 0.0081        | 79.3 | + EO Post       | $\\underline{0.2352}$ | 0.0027        | 0.1118        | 0.0054        | 88.6 |\n| + NSP Post      | 0.2353        | 0.0641        | 0.0369        | 0.0468        | 29.9 | + NEO Post      | 0.2349        | 0.0105        | 0.0706        | 0.0182        | 81.6 |\n| + SP&NSP Post   | 0.2376        | 0.0226        | 0.0221        | 0.0224        | 44.4 | + EO&NEO Post   | 0.2333        | 0.0021        | 0.0766        | 0.0041        | 88.4 |\n| MOOMTL          | 0.2256        | $\\underline{0.0032}$ | $\\underline{0.0092}$ | $\\underline{0.0048}$ | 70.8 | MOOMTL          | 0.2106        | $\\underline{0.0015}$ | 0.1060        | $\\underline{0.0029}$ | 89.2 |\n| Ours (region 0) | 0.2135        | 0.0680        | 0.0201        | 0.0310        | 16.4 | Ours (region 0) | 0.1090        | 0.1782        | 0.1030        | 0.1305        | 30.0 |\n| Ours (region 1) | 0.2383        | 0.0214        | 0.0128        | 0.0160        | 30.9 | Ours (region 1) | 0.2065        | 0.0663        | **0.0338**    | 0.0448        | 27.0 |\n| Ours (region 2) | **0.2405**    | 0.0134        | 0.0120        | 0.0126        | 41.9 | Ours (region 2) | 0.1871        | 0.0353        | $\\underline{0.0457}$ | 0.0398        | 52.3 |\n| Ours (region 3) | $\\underline{0.2397}$ | 0.0152        | 0.0294        | 0.0201        | 62.6 | Ours (region 3) | 0.2200        | 0.0443        | 0.0694        | 0.0541        | 57.5 |\n| Ours (region 4) | 0.2155        | **0.0019**    | **0.0081**    | **0.0031**    | 76.6 | Ours (region 4) | 0.2347        | **0.0013**    | 0.1123        | **0.0026**    | 89.3 |"}]

Author rebuttal:
We sincerely thank all the reviewers for valuable comments and suggestions! Below we have tried our best to address the concerns point-to-point for each reviewer, and we are looking forward for further discussion about our work. In addition, we have uploaded a page of supplementary material here, which contains some additional experimental results as suggested by reviewer cJkK and PYwN.

Meta-review: The paper proposes new social attribute-aware item-side group fairness (IGF) metrics to account for influence of users' social attributes on item exposure utility. The paper extends existing item side fairness notions in recommender systems to incorporate social utility that is derived from a user's neighbors in the social network. In the scenarios where social utility impacts exposure of items indirectly (as compared to recommendations themselves), the existing notions of fairness see limitations and the proposed methods claims to fix that. The reviewers appreciated that the paper validates the proposed metrics and approach with extensive experiments on real datasets that show effectiveness of the proposed flexible and controllable approach. However, reviewers raised some concerns. There were some concerns about the clarity of the paper that the authors are advised to carefully consider for a final version. It might help readability if non-standard acronyms (MOOMTL, NSP Reg, NSP Post, etc.) are used sparingly since they are harder to keep track of throughout the paper. 
Thank you for addressing the questions asked by the reviewers in their initial reviews. Please make changes to the paper and appendices accordingly, including adding the new experimental results that were shared in the discussion.
Decision: Accept (poster)