{"type":"ScholarlyArticle","title":"Α Descent-based Method on the Duality Gap for Solving Zero-sum Games","authors":[{"name":"Michail Fasoulakis","slug":"michail-fasoulakis","given":"Michail","family":"Fasoulakis","affiliation":""},{"name":"Evangelos Markakis","slug":"evangelos-markakis","given":"Evangelos","family":"Markakis","affiliation":""},{"name":"Georgios Roussakis","slug":"georgios-roussakis","given":"Georgios","family":"Roussakis","affiliation":""},{"name":"Christodoulos Santorinaios","slug":"christodoulos-santorinaios","given":"Christodoulos","family":"Santorinaios","affiliation":""}],"abstract":"We focus on the design of algorithms for finding equilibria in 2-player zero-sum games. Although it is well known that such problems can be solved by a single linear program, there has been a surge of interest in recent years for simpler algorithms, motivated in part by applications in machine learning. Our work proposes such a method, inspired by the observation that the duality gap (a standard metric for evaluating convergence in min-max optimization problems) is a convex function for bilinear zero-sum games. To this end, we analyze a descent-based approach, variants of which have also been used as a subroutine in a series of algorithms for approximating Nash equilibria in general non-zero-sum games.    \r\nIn particular, we study a steepest descent approach, by finding the direction that minimises the directional derivative of the duality gap function.\r\nOur main theoretical result is that the derived algorithms achieve a geometric decrease in the duality gap until we reach an approximate equilibrium. Finally, we complement this with an experimental evaluation, which provides promising findings. Our algorithm is comparable with (and in some cases outperforms) some of the standard approaches for solving 0-sum games, such as OGDA (Optimistic Gradient Descent/Ascent), even with thousands of available strategies per player.","doi":"10.24963/ijcai.2025/427","url":"https://ijcai.org/proceedings/2025/427","pdf":"https://ijcai.org/proceedings/2025/0427.pdf","markdown":"https://ijcai.org/proceedings/2025/427.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/427","volume":{"slug":"2025","title":"Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2025","url":"https://ijcai.org/proceedings/2025/","year":2025,"location":"Montreal, Canada","dates":"16-22 August 2025","editors":"James Kwok","isbn":"978-1-956792-06-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2025"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":427,"pages":{"first":3839,"last":3847},"keywords":["Machine Learning: ML: Game Theory","Game Theory and Economic Paradigms: GTEP: Noncooperative games","Game Theory and Economic Paradigms: GTEP: Other"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}