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Shapley value is a classic notion from game theory, historically used to quantify the contributions of individuals within groups, and more recently applied to assign values to data points when training machine learning models. Despite its…

Machine Learning · Computer Science 2020-02-28 Amirata Ghorbani , Michael P. Kim , James Zou

In many multi-agent settings, participants can form teams to achieve collective outcomes that may far surpass their individual capabilities. Measuring the relative contributions of agents and allocating them shares of the reward that…

Machine Learning · Computer Science 2022-08-19 Daphne Cornelisse , Thomas Rood , Mateusz Malinowski , Yoram Bachrach , Tal Kachman

Data valuation is an essential task in a data marketplace. It aims at fairly compensating data owners for their contribution. There is increasing recognition in the machine learning community that the Shapley value -- a foundational…

Cryptography and Security · Computer Science 2023-02-20 Zhihua Tian , Jian Liu , Jingyu Li , Xinle Cao , Ruoxi Jia , Jun Kong , Mengdi Liu , Kui Ren

While Explainable Artificial Intelligence (XAI) is increasingly expanding more areas of application, little has been applied to make deep Reinforcement Learning (RL) more comprehensible. As RL becomes ubiquitous and used in critical and…

Artificial Intelligence · Computer Science 2021-10-05 Alexandre Heuillet , Fabien Couthouis , Natalia Díaz-Rodríguez

Explainable artificial intelligence (XAI) is essential for trustworthy machine learning (ML), particularly in high-stakes domains such as healthcare and finance. Shapley value (SV) methods provide a principled framework for feature…

Machine Learning · Statistics 2025-10-03 Wangxuan Fan , Siqi Li , Doudou Zhou , Yohei Okada , Chuan Hong , Molei Liu , Nan Liu

This study introduces the \emph{edge-based Shapley value}, a novel allocation rule within cooperative game theory, specifically tailored for networked systems, where value is generated through interactions represented by edges. Traditional…

Computer Science and Game Theory · Computer Science 2025-07-17 Taiki Yamada , Taisuke Matsubae , Tomoya Akamatsu

Designing fair compensation mechanisms for demand response (DR) is challenging. This paper models the problem in a game theoretic setting and designs a payment distribution mechanism based on the Shapley Value. As exact computation of the…

Computer Science and Game Theory · Computer Science 2014-03-27 Gearóid O'Brien , Abbas El Gamal , Ram Rajagopal

Federated learning (FL) has emerged as a pivotal approach in machine learning, enabling multiple participants to collaboratively train a global model without sharing raw data. While FL finds applications in various domains such as…

Machine Learning · Computer Science 2024-06-04 Nurbek Tastan , Samar Fares , Toluwani Aremu , Samuel Horvath , Karthik Nandakumar

Shapley values originated in cooperative game theory but are extensively used today as a model-agnostic explanation framework to explain predictions made by complex machine learning models in the industry and academia. There are several…

Machine Learning · Statistics 2024-04-15 Lars Henry Berge Olsen , Ingrid Kristine Glad , Martin Jullum , Kjersti Aas

Model interpretability is one of the most intriguing problems in most of the Machine Learning models, particularly for those that are mathematically sophisticated. Computing Shapley Values are arguably the best approach so far to find the…

Machine Learning · Statistics 2022-04-15 Indranil Basu , Subhadip Maji

The Shapley value is the prevalent solution for fair division problems in which a payout is to be divided among multiple agents. By adopting a game-theoretic view, the idea of fair division and the Shapley value can also be used in machine…

Computer Science and Game Theory · Computer Science 2026-05-13 Guilherme Dean Pelegrina , Patrick Kolpaczki , Eyke Hüllermeier

When using machine learning techniques in decision-making processes, the interpretability of the models is important. In the present paper, we adopted the Shapley additive explanation (SHAP), which is based on fair profit allocation among…

Machine Learning · Computer Science 2022-03-03 Yasunobu Nohara , Koutarou Matsumoto , Hidehisa Soejima , Naoki Nakashima

Collaborative learning enables multiple participants to learn a single global model by exchanging focused updates instead of sharing data. One of the core challenges in collaborative learning is ensuring that participants are rewarded…

Machine Learning · Computer Science 2025-07-15 Nurbek Tastan , Samuel Horvath , Karthik Nandakumar

The Shapley value, which is arguably the most popular approach for assigning a meaningful contribution value to players in a cooperative game, has recently been used intensively in explainable artificial intelligence. Its meaningfulness is…

Machine Learning · Computer Science 2024-01-31 Patrick Kolpaczki , Viktor Bengs , Maximilian Muschalik , Eyke Hüllermeier

The value and copyright of training data are crucial in the artificial intelligence industry. Service platforms should protect data providers' legitimate rights and fairly reward them for their contributions. Shapley value, a potent tool…

Machine Learning · Computer Science 2025-11-21 Haifeng Sun , Yu Xiong , Runze Wu , Xinyu Cai , Changjie Fan , Lan Zhang , Xiang-Yang Li

Cooperative game is a critical research area in the multi-agent reinforcement learning (MARL). Global reward game is a subclass of cooperative games, where all agents aim to maximize the global reward. Credit assignment is an important…

Machine Learning · Computer Science 2022-10-14 Jianhong Wang , Yuan Zhang , Tae-Kyun Kim , Yunjie Gu

Social intelligence, the ability to navigate complex interpersonal interactions, presents a fundamental challenge for language agents. Training such agents via reinforcement learning requires solving the credit assignment problem:…

Artificial Intelligence · Computer Science 2026-04-22 Xiachong Feng , Yi Jiang , Xiaocheng Feng , Deyi Yin , Libo Qin , Yangfan Ye , Lei Huang , Weitao Ma , Yuxuan Gu , Chonghan Qin , Bing Qin , Lingpeng Kong

Explaining the predictions of opaque machine learning algorithms is an important and challenging task, especially as complex models are increasingly used to assist in high-stakes decisions such as those arising in healthcare and finance.…

Machine Learning · Computer Science 2022-06-29 David S. Watson

Shapley value is originally a concept in econometrics to fairly distribute both gains and costs to players in a coalition game. In the recent decades, its application has been extended to other areas such as marketing, engineering and…

Machine Learning · Statistics 2023-09-19 Liuqing Yang , Yongdao Zhou , Haoda Fu , Min-Qian Liu , Wei Zheng

As diffusion models are deployed in real-world settings, and their performance is driven by training data, appraising the contribution of data contributors is crucial to creating incentives for sharing quality data and to implementing…

Machine Learning · Computer Science 2025-03-05 Chris Lin , Mingyu Lu , Chanwoo Kim , Su-In Lee