Bilateral fair method for big language model recommendation system scene
By introducing a bilateral fairness method in the recommendation system of large language model, combining collaborative filtering and large language model generation embedding, and adopting interaction penalty factor and multi-object optimization strategy, the user and project fairness problems in the recommendation system are solved, achieving higher recommendation diversity and user trust.
Patent Information
- Application Number
- CN202510054695.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-14
- Publication Date
- 2025-05-09
- Estimated Expiration
- 2045-01-14
AI Technical Summary
There are problems of user fairness and project fairness in the large language model recommendation system, especially bilateral fairness issues, which have not been fully studied, resulting in poor recommendation quality for inactive users and unpopular projects and excessive recommendation of popular projects, limiting the diversity of the recommendation system.
A bilateral fairness method is proposed, by collecting user behavior data and project data, generating embeddings of users and projects, combining collaborative filtering and large language model, introducing penalties for interactions, and adopting a multi-objective optimization strategy to balance user fairness and project exposure fairness, and generating a final recommendation list.
It effectively alleviates the bilateral fairness problem in the recommendation system, ensures that different user groups and project categories have fair participation in the recommendation process, improves the diversity and accuracy of recommendations, and enhances user trust and the robustness of the system.
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Figure CN119961529A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of machine learning technology, and in particular to a bilateral fairness method for a large language model recommendation system scenario. Background Art
[0002] In recent years, with the rapid popularization of the Internet, the amount of data has increased day by day. Faced with the difficulty of processing massive amounts of data, recommendation systems have emerged. Recommendation systems cover almost every aspect of our lives, from e-commerce, multimedia to the selection of educational courses. Recommendation systems estimate users' interests and preferences through their historical interaction information and provide them with personalized recommendations, thereby improving the efficiency and accuracy of recommendations. Although recommendation systems have become one of the most successful cases of artificial intelligence practice, some work has pointed out that recommendation systems still have different types of fairness issues. Some work focuses on the unfairness of projects, focusing on the popularity bias in recommendations, that is, popular projects will get more exposure opportunities than less popular projects. This problem mainly comes from the fact that when training the model, popular projects will get more attention because they have more interaction data than less popular projects, so the model may be more inclined to recommend these products; another part of the work focuses on the unfairness of the user side. Here, users are divided into active user groups and inactive user groups according to their activity in the system. Generally speaking, the system works better on active users than inactive users. This may be because when training the model, users who interact more frequently with the platform will generate more interaction data than those who interact less frequently, so the model will pay more attention to and understand the preferences of these users. This differential treatment, such as differences in item exposure and user performance caused by data heterogeneity, will produce personal economic differences and even amplify inherent biases in the model.
[0003] In order to better distinguish these unfair issues, existing research works divide them into user fairness, project fairness and bilateral fairness according to the research objects. Among them, user fairness is divided into individual fairness and group fairness. The former emphasizes that the model pays equal attention to the personalized preferences of each user, and the latter emphasizes that user groups with different attributes should be treated equally by the model. Most of the existing works adopt methods such as adding regularization terms, constrained optimization, and balancing data sets; project fairness also has individual fairness and group fairness, which is usually reflected in the proportion of individuals and groups in the recommendation list. Most of the work is achieved by proposing new fair re-ranking algorithms and reinforcement learning; bilateral fairness refers to considering user fairness and project fairness at the same time, and most of the current work adopts the addition of regularization and constraints.
[0004] With the rapid development of large language models, more and more studies have begun to explore their combination with recommendation systems, giving rise to the emergence of large language model recommendation systems. This type of recommendation system has stronger understanding and generation capabilities. It can not only make recommendations based on user behavior data, but also deeply explore user needs through technologies such as natural language processing and dialogue modeling, thereby generating more personalized recommendations. However, compared with traditional recommendation systems, the fairness issue in large language model recommendation systems is more complicated. Large language models can generate personalized recommendations by understanding users' multi-round conversations, emotional tendencies, language expressions and other information. This flexible modeling method provides more recommendation possibilities for inactive users, because even if there is a lack of sufficient behavioral data, the model can infer user interests through language and context. However, since large language models rely on training data, some user groups (such as inactive users or cold start users) may have poor recommendation quality, or some user features may be overfitted, causing unfairness. In addition, large language models are usually able to comprehensively analyze users' historical data, current context, and text descriptions of items (such as product information, movie plots, etc.) to generate personalized recommendations for each user. However, the exposure problem of items still exists. Since popular items usually have more interaction data and a broad audience base, they tend to be recommended first, which may cause unpopular items to fail to receive enough attention, thus limiting the diversity of the recommendation system.
[0005] Although many studies have been conducted on large language model recommendation systems, these works focus more on performance improvement, especially in terms of recommendation accuracy, personalized recommendation quality, and system response speed. Only a few works have paid attention to the fairness issues in large language model recommendation systems, which are the same as traditional recommendation systems. These works only focus on user fairness or project fairness, and lack research on bilateral fairness issues. Therefore, how to design a bilateral fairness method that can simultaneously alleviate user fairness and project fairness issues in large language model recommendation systems has become an urgent problem to be solved in this field. Summary of the invention
[0006] In order to solve the technical problems existing in the above-mentioned prior art, the present invention proposes a bilateral fairness method for the large language model recommendation system scenario, which can effectively alleviate the bilateral fairness problem of the recommendation system while maintaining the overall performance of the large language model recommendation system.
[0007] To achieve the above object, the present invention provides a bilateral fairness method for a large language model recommendation system scenario, comprising:
[0008] Collecting user behavior data and project data, wherein the user behavior data includes user interaction information on projects, and the project data includes detailed information of each project;
[0009] Processing the user behavior data and the project data to generate preliminary embeddings of users, preliminary embeddings of projects, and similar user embeddings, respectively;
[0010] Generate enhanced embeddings for users and items using a large language model;
[0011] Fusing the preliminary embedding of the user, the similar user embedding and the enhanced embedding of the user to generate a fused user embedding, and fusing the preliminary embedding of the item with the enhanced embedding of the item to generate a fused item embedding;
[0012] Performing a dot product operation on the fused user embedding and the fused item embedding to obtain a recommendation score, introducing an interaction count penalty factor to process the recommendation score to obtain a weighted recommendation score;
[0013] The weighted recommendation scores are processed through a bilateral fairness optimization strategy to generate a final recommendation list.
[0014] Preferably, generating the preliminary embedding of the user and the preliminary embedding of the project comprises:
[0015] The collaborative filtering method is used to process each user behavior data and project data respectively to obtain the preliminary embedding of the user and the preliminary embedding of the project.
[0016] Preferably, generating the similar user embedding includes:
[0017] The similar user embedding is generated by calculating the similarity between the user behavior data, specifically:
[0018]
[0019] In the formula, Embedding for similar users, u i represents user i,u j represents user j, Sim(u i ,u j ) represents user u i with u j The similarity between For user u j The initial embedding of Top-K(u i ) indicates that the i The K most similar users.
[0020] Preferably, the fused user embedding and the fused item embedding are generated by using a weighted average method or a splicing method;
[0021] Wherein, the weighted average method is:
[0022]
[0023] In the formula, α, β, γ and α ′ , β ′ are all hyperparameters, To integrate user embedding, For user u i The initial embedding of Embedding for similar users, For user u i Enhanced embedding of Embedded for fusion projects, For project i j The initial embedding of For project i j Enhanced embedding of
[0024] The splicing method is:
[0025]
[0026] Here, concat means concatenating multiple embedding vectors into a larger embedding.
[0027] Preferably, the interaction number penalty factor is:
[0028]
[0029] In the formula, c j Indicates project i j The number of interactions by all users, c min and c max Respectively represent the minimum and maximum number of interactions of all items, P j is the penalty factor for the number of interactions, and δ is the scaling factor.
[0030] Preferably, obtaining the weighted recommendation score includes:
[0031] y i ′ j =y ij ·P j ;
[0032] In the formula, y ij Represents user u i For Project I j The original recommendation score, y i ′ j is the weighted recommendation score.
[0033] Preferably, the bilateral fairness optimization strategy includes:
[0034] Quantify the user unfairness index and the project exposure unfairness index, comprehensively consider the recommendation score, user fairness and project exposure fairness, and obtain a multi-objective optimization function;
[0035] Wherein, the multi-objective optimization function is:
[0036]
[0037] In the formula, λ1 and λ2 are adjustment coefficients used to balance the relationship between score maximization and fairness optimization. is a multi-objective optimization function, ΔNDCG is the performance index difference between the active user group and the inactive user group, ΔExposure is the exposure difference between the popular items and the unpopular items in the recommendation list, and y i ′ j is the weighted recommendation score, N is the number of users, and M is the number of items.
[0038] Preferably, quantifying the user unfairness indicator includes:
[0039] ΔNDCG=|NDCG(u active )-NDCG(u inactive )|;
[0040] In the formula, NDCG(u active ) and NDCG(u inactive ) represent the NDCG values of active users and inactive users respectively;
[0041] Quantifying project exposure unfairness indicators includes:
[0042] ΔExposure=|Exposure popular -Exposure cold |;
[0043] Where, Exposure popular and Exposure cold Respectively represent the proportion of popular projects and unpopular projects in the recommendation list.
[0044] Preferably, the final recommendation list is:
[0045]
[0046] In the formula, For user u i The final recommendation list contains the items after fairness optimization; Rank() is the sorting function.
[0047] Compared with the prior art, the present invention has the following advantages and technical effects:
[0048] (1) This invention effectively alleviates the bias problem in the recommendation system by introducing a bilateral optimization strategy of user fairness and project fairness. Compared with traditional methods, this method can accurately identify and adjust unfair phenomena, ensuring that different user groups and project categories can participate in the recommendation process fairly. It achieves a significant balance between diversity and fairness, improves users' trust and satisfaction with the system, and contributes to the long-term healthy development of the platform;
[0049] (2) This paper combines collaborative filtering embedding and large language model embedding to propose a more expressive embedding generation method that organically integrates user behavior with project text information. By adding similar user embeddings, the user's potential preferences are further explored, making the recommendation results more diverse and accurate. In addition, in the process of generating the recommendation list, a re-ranking algorithm with the number of interactions as a penalty factor is designed to reduce the excessive bias of popular projects, thereby increasing the exposure opportunities of unpopular projects, and enhancing the diversity of recommendations while ensuring the quality of recommendations;
[0050] (3) The present invention adopts a multi-objective optimization method, combining the maximization of recommendation scores with bilateral fairness optimization, and flexibly adapts to the needs of different scenarios by adjusting the hyperparameter weights. This method can not only dynamically balance the quality and fairness of recommendations, but also has strong scalability and is suitable for the deployment of various recommendation systems. Through this optimization mechanism, the platform can ensure that the recommendation system has higher robustness and fairness while meeting the personalized needs of users, thereby improving the overall user experience and ecosystem vitality. BRIEF DESCRIPTION OF THE DRAWINGS
[0051] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:
[0052] Figure 1 A flowchart of a bilateral fairness method for a large language model recommendation system scenario according to an embodiment of the present invention;
[0053] Figure 2 A framework diagram of a large language model recommendation system for alleviating bilateral fairness issues according to an embodiment of the present invention;
[0054] Figure 3 It is a schematic diagram of improved embedding fusion enhancement according to an embodiment of the present invention;
[0055] Figure 4 This is an improved multi-objective optimization flowchart of an embodiment of the present invention. DETAILED DESCRIPTION
[0056] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.
[0057] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.
[0058] This embodiment proposes a bilateral fairness method for large language model recommendation system scenarios, such as Figure 1-Figure 2 ,include:
[0059] Collect user behavior data and project data, where user behavior data includes user interaction information on projects, and project data includes detailed information on each project;
[0060] Perform data processing on user behavior data and project data to generate preliminary embeddings for users, preliminary embeddings for projects, and similar user embeddings respectively;
[0061] Generate enhanced embeddings for users and items using a large language model;
[0062] Fusing the user's preliminary embedding, similar user embeddings, and the user's enhanced embedding to generate a fused user embedding, and fusing the item's preliminary embedding with the item's enhanced embedding to generate a fused item embedding;
[0063] Perform dot product operation on the fused user embedding and the fused item embedding to obtain the recommendation score, introduce the interaction number penalty factor to process the recommendation score, and obtain the weighted recommendation score;
[0064] The weighted recommendation scores are processed through the bilateral fairness optimization strategy to generate the final recommendation list.
[0065] This embodiment first collects user behavior data and project data and generates preliminary embeddings of users and preliminary embeddings of projects; secondly, similar user embeddings are generated based on similarity calculation; then, enhanced embeddings of users and projects are generated using a large language model, and merged with the embeddings generated by collaborative filtering; then, an interaction penalty factor is introduced to reduce over-recommendations of popular projects; then, user fairness and project exposure fairness are balanced through a bilateral fairness optimization strategy; finally, a final recommendation list is generated to improve the accuracy, diversity and fairness of recommendations, ensuring that the fairness requirements of users and projects are met while maximizing the recommendation score.
[0066] Specifically, in the recommendation system of this embodiment, it is necessary to first collect user behavior data and project information. User behavior data includes user interaction information on projects, including clicks, ratings, etc. Project data includes detailed information of each project, such as title, description, category, etc.
[0067] Assuming there are N users and M items, the user behavior data can be expressed as:
[0068]
[0069] In the formula, u i represents user i, i j Represents project j, r ij Represents user u i For Project I j Feedback value, D user Represents user behavior data. In this embodiment, the user behavior data set is used to train and verify the recommendation model.
[0070] Furthermore, generating preliminary embeddings of users and items includes:
[0071] The collaborative filtering method is used to process each user behavior data and project data respectively to obtain the preliminary embedding of the user and the preliminary embedding of the project.
[0072] Specifically, assuming that the embedding of each user and item is obtained through a matrix decomposition algorithm, the preliminary embedding of the user is generated through the interaction data between the user and the item and initial embedding of the project These preliminary embeddings are the basis of the recommender system and reflect the interaction history characteristics of users and items.
[0073] Furthermore, similar user embeddings are generated, including:
[0074] Calculate the similarity between the user behavior data and generate the similar user embedding, specifically:
[0075]
[0076] In the formula, Embedding for similar users, u i represents user i,u j represents user j, Sim(u i ,u j ) represents user u i with u j The similarity between For user u j The initial embedding of Top-K(u i ) indicates that the iThe K most similar users.
[0077] Specifically, the cosine similarity calculation method is used in this embodiment:
[0078]
[0079] Among them, Sim(u i ,u j ) represents user u i with u j The similarity between For user u i Initial embedding of .
[0080] Furthermore, if Figure 3 , using the large language model to generate enhanced embeddings for users and items. The large language model generates richer semantic embeddings by parsing the user's behavior history and the text information of the item. For example, for user u i , user behavior sequences, such as items clicked, content rated, etc., can be input into the large language model to obtain the user's enhanced embedding Similarly, text descriptions of items, such as title, category, introduction, etc., can be input into the large language model to obtain an enhanced embedding of the item
[0081] The user's preliminary embedding, similar user embedding and user's enhanced embedding are fused to generate a fused user embedding, and the item's preliminary embedding and item's enhanced embedding are fused to generate a fused item embedding;
[0082] In order to make full use of collaborative filtering and embedding generated by a large language model, this embodiment combines them by weighted averaging or concatenation:
[0083] Among them, the weighted average method is:
[0084]
[0085] In the formula, α, β, γ and α ′ , β ′ are all hyperparameters, To integrate user embedding, For user u i The initial embedding of Embedding for similar users, For user u i Enhanced embedding of Embedded for fusion projects, For project i j The initial embedding of For project i j Enhanced embedding of
[0086] The splicing method is:
[0087]
[0088] Here, concat means concatenating multiple embedding vectors into a larger embedding.
[0089] This embodiment combines collaborative filtering embedding and large language model embedding to propose a more expressive embedding generation method that organically integrates user behavior with project text information. By adding similar user embeddings, the user's potential preferences are further explored, making the recommendation results more diverse and accurate. In addition, in the process of generating the recommendation list, a re-ranking algorithm with the number of interactions as a penalty factor is designed to reduce the excessive bias of popular projects, thereby increasing the exposure opportunities of unpopular projects, and enhancing the diversity of recommendations while ensuring the quality of recommendations.
[0090] Furthermore, in order to reduce over-recommendation of popular items, this embodiment introduces an interaction penalty factor. The interaction penalty factor is:
[0091]
[0092] In the formula, c j Indicates project i j The number of interactions by all users, c min and c max Respectively represent the minimum and maximum number of interactions of all items, P j is the penalty factor for the number of interactions, and δ is the scaling factor, which is used to control the impact of the number of interactions on the penalty factor.
[0093] Furthermore, obtaining the weighted recommendation score includes:
[0094] y i ′ j =y ij ·P j ;
[0095] In the formula, y ij Represents user u i For Project I j The original recommendation score, y i ′ j is the weighted recommendation score.
[0096] Specifically, when generating the recommendation score, the penalty factor is added to the original score, thereby reducing the recommendation score for popular items and increasing the recommendation score for unpopular items, thereby improving the ranking of unpopular items in the recommendation list and increasing the recommendation exposure of unpopular items.
[0097] Furthermore, if Figure 4 , which is an improved multi-objective optimization flowchart of this embodiment. In order to alleviate unfairness while ensuring the overall performance of the large language model recommendation system, this embodiment introduces a bilateral fairness optimization strategy, which optimizes user fairness and project exposure fairness respectively while maximizing the recommendation score.
[0098] The bilateral fairness optimization strategies include:
[0099] Quantify the user unfairness index and the project exposure unfairness index, comprehensively consider the recommendation score, user fairness and project exposure fairness, and obtain a multi-objective optimization function;
[0100] Among them, the multi-objective optimization function is:
[0101]
[0102] In the formula, λ1 and λ2 are adjustment coefficients used to balance the relationship between score maximization and fairness optimization. is a multi-objective optimization function, ΔNDCG is the performance index difference between the active user group and the inactive user group, ΔExposure is the exposure difference between the popular items and the unpopular items in the recommendation list, and y i ′ j is the weighted recommendation score, N is the number of users, and M is the number of items.
[0103] Specifically, the quantification of user unfairness indicators includes:
[0104] ΔNDCG=|NDCG(u active )-NDCG(u inactive )|;
[0105] In the formula, NDCG(u active ) and NDCG(u inactive ) represent the NDCG values of active users and inactive users respectively;
[0106] Quantifying project exposure unfairness indicators includes:
[0107] ΔExposure=|Exposure popular -Exposure cold |;
[0108] Where, Exposure popular and Exposure cold Respectively represent the proportion of popular projects and unpopular projects in the recommendation list.
[0109] Furthermore, after bilateral fairness optimization, the final recommendation list is generated by sorting:
[0110]
[0111] In the formula, For user u i The final recommendation list contains the items after fairness optimization; Rank() is a sorting function, which uses the recommendation score y i ′ j Sort.
[0112] This embodiment effectively alleviates the bias problem in the recommendation system by introducing a bilateral optimization strategy of user fairness and project fairness. Compared with traditional methods, the method of this embodiment can accurately identify and adjust unfairness, ensuring that different user groups and project categories can participate in the recommendation process fairly. It achieves a significant balance between diversity and fairness, improves users' trust and satisfaction with the system, and contributes to the long-term healthy development of the platform.
[0113] This embodiment adopts a multi-objective optimization method, combining the maximization of recommendation scores with bilateral fairness optimization, and flexibly adapts to the needs of different scenarios by adjusting the hyperparameter weights. This method can not only dynamically balance the quality and fairness of recommendations, but also has strong scalability and is suitable for the deployment of various recommendation systems. Through this optimization mechanism, the platform can ensure that the recommendation system has higher robustness and fairness while meeting the personalized needs of users, thereby improving the overall user experience and ecosystem vitality.
[0114] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.
Claims
1. A bilateral fairness method for large language model recommendation system scenarios, characterized in that: include: Collecting user behavior data and project data, wherein the user behavior data includes user interaction information on projects, and the project data includes detailed information of each project; Processing the user behavior data and the project data to generate preliminary embeddings of users, preliminary embeddings of projects, and similar user embeddings, respectively; Generate enhanced embeddings for users and items using a large language model; Fusing the preliminary embedding of the user, the similar user embedding and the enhanced embedding of the user to generate a fused user embedding, and fusing the preliminary embedding of the item with the enhanced embedding of the item to generate a fused item embedding; Performing a dot product operation on the fused user embedding and the fused item embedding to obtain a recommendation score, introducing an interaction count penalty factor to process the recommendation score to obtain a weighted recommendation score; The weighted recommendation scores are processed through a bilateral fairness optimization strategy to generate a final recommendation list.
2. The bilateral fairness method for large language model recommendation system scenario according to claim 1, characterized in that: Generating a preliminary embedding of the user and a preliminary embedding of the item, including: The collaborative filtering method is used to process each user behavior data and project data respectively to obtain the preliminary embedding of the user and the preliminary embedding of the project.
3. The bilateral fairness method for large language model recommendation system scenario according to claim 1, characterized in that: Generating the similar user embedding includes: The similar user embedding is generated by calculating the similarity between the user behavior data, specifically: In the formula, Embedding for similar users, u i represents user i,u j represents user j, Sim(u i ,u j ) represents user u i with u j The similarity between For user u j The initial embedding of Top-K(u i ) indicates that the i The K most similar users.
4. The bilateral fairness method for large language model recommendation system scenario according to claim 3, characterized in that: Generate the fused user embedding and the fused item embedding by using a weighted average method or a splicing method; Wherein, the weighted average method is: In the formula, α, β, γ and α ′ , β ′ are all hyperparameters, To integrate user embedding, For user u i The initial embedding of Embedding for similar users, For user u i Enhanced embedding of Embedded for fusion projects, For project i j The initial embedding of For project i j Enhanced embedding of The splicing method is: Here, concat means concatenating multiple embedding vectors into a larger embedding.
5. The bilateral fairness method for large language model recommendation system scenario according to claim 1, characterized in that: The interaction number penalty factor is: In the formula, c j Indicates project i j The number of times it is interacted by all users, c min and c max Respectively represent the minimum and maximum number of interactions of all items, P j is the penalty factor for the number of interactions, and δ is the scaling factor.
6. The two-sided fairness method for large language model recommendation system scenario according to claim 5, characterized in that: Obtaining the weighted recommendation score includes: and i ′ j =and ij ·P j ; In the formula, y ij Represents user u i For Project I j The original recommendation score, y i ′ j is the weighted recommendation score.
7. The bilateral fairness method for large language model recommendation system scenario according to claim 1, characterized in that: The bilateral fairness optimization strategy includes: Quantify the user unfairness index and the project exposure unfairness index, comprehensively consider the recommendation score, user fairness and project exposure fairness, and obtain a multi-objective optimization function; Wherein, the multi-objective optimization function is: In the formula, λ1 and λ2 are adjustment coefficients used to balance the relationship between score maximization and fairness optimization. is a multi-objective optimization function, ΔNDCG is the performance index difference between the active user group and the inactive user group, ΔExposure is the exposure difference between the popular items and the unpopular items in the recommendation list, and y i ′ j is the weighted recommendation score, N is the number of users, and M is the number of items.
8. The two-sided fairness method for large language model recommendation system scenario according to claim 7, characterized in that: Quantifying user unfairness indicators includes: ΔNDCG=|NDCG(u active )-NDCG(u inactive )|; In the formula, NDCG(u active ) and NDCG(u inactive ) represent the NDCG values of active users and inactive users respectively; Quantifying project exposure unfairness indicators includes: ΔExposure=|Exposure popular -Exposure cold |; Where, Exposure popular and Exposure cold Respectively represent the proportion of popular projects and unpopular projects in the recommendation list.
9. The bilateral fairness method for large language model recommendation system scenario according to claim 8, characterized in that: The final recommendation list is: In the formula, For user u i The final recommendation list contains the items after fairness optimization; Rank() is the sorting function.
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