{"type":"ScholarlyArticle","title":"Approximating the Shapley Value Using Stratified Empirical Bernstein Sampling","authors":[{"name":"Mark A. Burgess","slug":"mark-a-burgess","given":"Mark A.","family":"Burgess","affiliation":""},{"name":"Archie C. Chapman","slug":"archie-c-chapman","given":"Archie C.","family":"Chapman","affiliation":""}],"abstract":"The Shapley value is a well recognised method for dividing the value of joint effort in cooperative games. However, computing the Shapley value is known to be computationally hard, so stratified sample-based estimation is sometimes used. For this task, we provide two contributions to the state of the art. First, we derive a novel concentration inequality that is tailored to stratified Shapley value estimation using sample variance information. Second, by sequentially choosing samples to minimize our inequality, we develop a new and more efficient method of sampling to estimate the Shapley value. We evaluate our sampling method on a suite of test cooperative games, and our results demonstrate that it outperforms or is competitive with existing stratified sample-based estimation approaches to computing the Shapley value.","doi":"10.24963/ijcai.2021/11","url":"https://ijcai.org/proceedings/2021/11","pdf":"https://ijcai.org/proceedings/2021/0011.pdf","markdown":"https://ijcai.org/proceedings/2021/11.md","bibtex":"https://ijcai.org/proceedings/2021/bibtex/11","volume":{"slug":"2021","title":"Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2021","url":"https://ijcai.org/proceedings/2021/","year":2021,"location":"Montreal","dates":"19-27 August 2021","editors":"Prof. Zhi-Hua Zhou","isbn":"978-0-9992411-9-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2021"},"section":"Agent-based and Multi-agent Systems","track":"Main Track","number":11,"pages":{"first":73,"last":81},"keywords":["Agent-based and Multi-agent Systems: Cooperative Games","Uncertainty in AI: Uncertainty Representations"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}