eprintid: 50822 rev_number: 5 eprint_status: archive userid: 1482 importid: 105 dir: disk0/00/05/08/22 datestamp: 2025-05-02 07:15:14 lastmod: 2025-05-02 07:18:48 status_changed: 2025-05-02 07:15:14 type: article metadata_visibility: show creators_name: De Montbrun, Etienne creators_name: Renault, Jerôme creators_idrefppn: 280147740 creators_idrefppn: 112479952 creators_halaffid: 1002422 creators_halaffid: 1002422 title: Optimistic Gradient Descent Ascent in General-Sum Bilinear Games ispublished: pub subjects: subjects_ECO abstract: We study the convergence of optimistic gradient descent ascent in unconstrained bilinear games. For zero-sum games, we prove exponential convergence to a saddle-point for any payoff matrix, and provide the exact ratio of convergence as a function of the step size. Then, we introduce OGDA for general-sum games and show that, in many cases, either OGDA converges exponentially fast to a Nash equilibrium, or the payoffs for both players converge to . We also show how to increase drastically the speed of convergence of a zero-sum problem by introducing a general-sum game using the Moore-Penrose inverse of the original payoff matrix. To our knowledge, this shows for the first time that general-sum games can be used to optimally improve algorithms designed for min-max problems. We illustrate our results on a toy example of a Wasserstein GAN. Finally, we show how the approach could be extended to the more general class of "hidden bilinear games". date: 2025-07 date_type: published publisher: American Institute of Mathematical Science id_number: 10.3934/jdg.2024030 official_url: http://tse-fr.eu/pub/130526 faculty: tse divisions: tse language: en has_fulltext: FALSE doi: 10.3934/jdg.2024030 view_date_year: 2025 full_text_status: none publication: Journal of Dynamics and Games volume: vol 12 number: n° 3 place_of_pub: Springfield pagerange: 267-301 refereed: TRUE issn: 2164-6066 oai_identifier: oai:tse-fr.eu:130526 harvester_local_overwrite: number harvester_local_overwrite: volume harvester_local_overwrite: creators_name harvester_local_overwrite: pending harvester_local_overwrite: creators_idrefppn harvester_local_overwrite: creators_halaffid harvester_local_overwrite: publisher harvester_local_overwrite: place_of_pub harvester_local_overwrite: hal_id harvester_local_overwrite: hal_version harvester_local_overwrite: hal_url harvester_local_overwrite: hal_passwd oai_lastmod: 2025-04-29T09:12:59Z oai_set: tse site: ut1 hal_id: hal-05053682 hal_passwd: 57sicf hal_version: 1 hal_url: https://hal.science/hal-05053682 citation: De Montbrun, EtienneIdRef and Renault, JerômeIdRef (2025) Optimistic Gradient Descent Ascent in General-Sum Bilinear Games. Journal of Dynamics and Games, vol 12 (n° 3). pp. 267-301.